Precalculus (10th Edition)
10th Edition
ISBN: 9780321979070
Author: Michael Sullivan
Publisher: PEARSON
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Textbook Question
Chapter 7.2, Problem 46AYU
In Problems 45–56, use a calculator to find the value of each expression rounded to two decimal places.
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4. Identify at least two mistakes in Francisco's work. Correct the mistakes and
complete the problem by using the second derivative test.
2f
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First Derivative Test or the Second Derivative Test.
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5. Identify at least three mistakes in Francisco's work. Then sketch the graph of the
function and label the local max and local min.
1. Find the equation of the tangent line to the curve
y=x-2x3+x-2 at the point (1.-2).
Sketch the araph of y=x42x3+x-2 and the tangent line at (1,-2)
y' = 4x-6x
y' (1) = 4(1) - 667 - 2
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Chapter 7 Solutions
Precalculus (10th Edition)
Ch. 7.1 - What is the domain and the range of y=sinx ? (p....Ch. 7.1 - A suitable restriction on the domain of the...Ch. 7.1 - If the domain of a one-to-one function is [ 3, ) ,...Ch. 7.1 - True or False The graph of y=cosx is decreasing on...Ch. 7.1 - 5. (pp. )
Ch. 7.1 - sin(6)=;cos=.(pp. 368377)Ch. 7.1 - y= sin 1 x means _____, where 1x1 and 2 y 2 .Ch. 7.1 - cos 1 (cosx)=x , where__________.Ch. 7.1 - Concepts and Vocabulary
9. where
Ch. 7.1 - Concepts and Vocabulary
10. True or False The...
Ch. 7.1 - True or False sin( sin 1 0 )=0 and cos( cos 1 0...Ch. 7.1 - True or False y= tan 1 x means x=tany , where x...Ch. 7.1 - Which of the following inequalities describes...Ch. 7.1 - . Choose the inverse function f1 of...Ch. 7.1 - In Problems 15-26, find, the exact value sin 1 0Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 15-26, find, the exact value of each...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 27-38, use a calculator to find the...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 39-62, find the exact value, if any,...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - In Problems 63-70, find the inverse function f 1...Ch. 7.1 - Find the exact solution of each equation. 4 sin 1...Ch. 7.1 - Find the exact solution of each equation. 2 cos 1...Ch. 7.1 - Find the exact solution of each equation. 3 cos 1...Ch. 7.1 - Find the exact solution of each equation. 6 sin 1...Ch. 7.1 - Find the exact solution of each equation. 3 tan 1...Ch. 7.1 - In Problems 71-78, find the exact solution of each...Ch. 7.1 - In Problems 71-78, find the exact solution of each...Ch. 7.1 - In Problems 71-78, find the exact solution of each...Ch. 7.1 - Applications and Extensions In Problems 7580, use...Ch. 7.1 - In Problems 79-84, use the following discussion....Ch. 7.1 - In Problems 79-84, use the following discussion....Ch. 7.1 - In Problems 79-84, use the following discussion....Ch. 7.1 - In Problems 79-84, use the following discussion....Ch. 7.1 - In Problems 79-84, use the following discussion....Ch. 7.1 - Being the First to See the Rising Sun Cadillac...Ch. 7.1 - Movie Theater Screens Suppose that a movie theater...Ch. 7.1 - Area under a Curve The area under the graph of y=...Ch. 7.1 - Area under a Curve The area under the graph of y=...Ch. 7.1 - Problems 89 and 90 require the following...Ch. 7.1 - Problems 89 and 90 require the following...Ch. 7.1 - Problems are based on material learned earlier in...Ch. 7.1 - State why the graph of the function f shown to the...Ch. 7.1 - The exponential function f( x )=1+ 2 x is...Ch. 7.1 - Problems 8998 are based on material learned...Ch. 7.2 - What is the domain and the range of y=secx ?Ch. 7.2 - True or False The graph of y=secx is one-to-one on...Ch. 7.2 - If tan= 1 2 , 2 2 , then sin= ______.Ch. 7.2 - y= sec 1 x means ________, where | x | ______ and...Ch. 7.2 - y= sec 1 x means ________, where | x | ______ and...Ch. 7.2 - True or False It is impossible to obtain exact...Ch. 7.2 - True or False csc 1 0.5 is not defined.Ch. 7.2 - True or False The domain of the inverse cotangent...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In problems , find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 936, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In problems , find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 9-36, find the exact value of each...Ch. 7.2 - In Problems 3744, find the exact value of each...Ch. 7.2 - In Problems 3744, find the exact value of each...Ch. 7.2 - In Problems 3744, find the exact value of each...Ch. 7.2 - In problems,, find the exact value of each...Ch. 7.2 - In problems , find the exact value of each...Ch. 7.2 - In Problems 3744, find the exact value of each...Ch. 7.2 - In Problems 3744, find the exact value of each...Ch. 7.2 - In Problems 3744, find the exact value of each...Ch. 7.2 - In Problems 4556, use a calcualtor to find the...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems , use a calculator to find the value...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems , use a calculator to find the value...Ch. 7.2 - In Problems 4556, use a calculator to find the...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 57-66, write each trigonometric...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - In Problems 67-78, f( x )=sinx , 2 x 2 , g( x...Ch. 7.2 - Problems 79 and 80 require the following...Ch. 7.2 - Problems 79 and 80 require the following...Ch. 7.2 - Artillery A projectile fired into the first...Ch. 7.2 - Using a graphing utility, graph
Ch. 7.2 - Using a graphing utility, graph
Ch. 7.2 - Using a graphing utility, graph y=csc1x.Ch. 7.2 - Explain in your own words how you would use your...Ch. 7.2 - Consult three texts on calculus and write down the...Ch. 7.2 - Find the complex zeros of f( x )= x 4 +21 x 2 100...Ch. 7.2 - Determine algebraically whether f(x)= x 3 + x 2 x...Ch. 7.2 - Convert 315 to radians.Ch. 7.2 - Find the length of the are subtended by a central...Ch. 7.3 - Solve: 3x5=x+1Ch. 7.3 - sin( 4 )= ______; cos( 8 3 )= ______.Ch. 7.3 - Find the real solutions of 4 x 2 x5=0 .Ch. 7.3 - Find the real solutions of x 2 x1=0 .Ch. 7.3 - Find the real solutions of ( 2x1 ) 2 3( 2x1 )4=0 .Ch. 7.3 - True or False Most trigonometric equations have...Ch. 7.3 - True or False Two solutions of the equation sin= 1...Ch. 7.3 - True or False The set of all solutions of the...Ch. 7.3 - True or False The equation sin=2 has a real...Ch. 7.3 - If all solutions of a trigonometric equation are...Ch. 7.3 - Suppose = 2 is the only solution of a...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 13-36, solve each equation on the...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems 37-46, solve each equation. Give a...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems use a calculator to solve each...Ch. 7.3 - In Problems 4758, use a calculator to solve each...Ch. 7.3 - In Problems 4758, use a calculator to solve each...Ch. 7.3 - In Problems 4758, use a calculator to solve each...Ch. 7.3 - In Problems 4758, use a calculator to solve each...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - Prob. 78AYUCh. 7.3 - Prob. 79AYUCh. 7.3 - Prob. 80AYUCh. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 59-82, solve each equation on the...Ch. 7.3 - In Problems 83-94, use a graphing utility to solve...Ch. 7.3 - In Problems 83-94, use a graphing utility to solve...Ch. 7.3 - Prob. 85AYUCh. 7.3 - Prob. 86AYUCh. 7.3 - Prob. 87AYUCh. 7.3 - Prob. 88AYUCh. 7.3 - In Problems 83-94, use a graphing utility to solve...Ch. 7.3 - Prob. 90AYUCh. 7.3 - In Problems 83-94, use a graphing utility to solve...Ch. 7.3 - Prob. 92AYUCh. 7.3 - Prob. 93AYUCh. 7.3 - In Problems 83-94, use a graphing utility to solve...Ch. 7.3 - What are the zeros of f( x )=4 sin 2 x3 on the...Ch. 7.3 - Prob. 96AYUCh. 7.3 - f(x)=3sinx a. Find the zeros of f on the interval...Ch. 7.3 - f( x )=2cosx a. Find the zeros of f on the...Ch. 7.3 - f( x )=4tanx a. Solve f( x )=4 . b. For what...Ch. 7.3 - Prob. 100AYUCh. 7.3 - Prob. 101AYUCh. 7.3 - Prob. 102AYUCh. 7.3 - a. Graph f( x )=4cosx and g( x )=2cosx+3 on the...Ch. 7.3 - Prob. 104AYUCh. 7.3 - Prob. 105AYUCh. 7.3 - The Ferris Wheel In 1893, George Ferris engineered...Ch. 7.3 - Holding Pattern An airplane is asked to slay...Ch. 7.3 - Projectile Motion A golfer hits a golf ball with...Ch. 7.3 - Heat Transfer In the study of heat transfer, the...Ch. 7.3 - Carrying a Ladder around a Corner Two hallways,...Ch. 7.3 - Projectile Motion The horizontal distance that a...Ch. 7.3 - Projectile Motion Refer to Problem 111. a. If you...Ch. 7.3 - sin 1 sin 2 = v 1 v 2 The ratio v 1 v 2 is...Ch. 7.3 - The index of refraction of light in passing from a...Ch. 7.3 - Ptolemy, who lived in the city of Alexandria in...Ch. 7.3 - Bending Light The speed of yellow sodium light...Ch. 7.3 - Bending Light A beam of light with a wavelength of...Ch. 7.3 - Bending Light A light ray with a wavelength of 589...Ch. 7.3 - Challenge Problem A light beam passes through a...Ch. 7.3 - Brewsters Law If the angle of incidence and the...Ch. 7.3 - Explain in your own words how you would use your...Ch. 7.3 - Explain why no further points of intersection (and...Ch. 7.3 - Convert 6 x =y to an equivalent statement...Ch. 7.3 - Find the zeros of f( x )=2 x 2 9x+8 .Ch. 7.3 - Prob. 125AYUCh. 7.3 - Prob. 126AYUCh. 7.4 - True or False sin 2 =1 cos 2Ch. 7.4 - True or False sin( )+cos( )=cossinCh. 7.4 - Suppose that fandg are two functions with the same...Ch. 7.4 - Prob. 4AYUCh. 7.4 - cos()cos= _____.Ch. 7.4 - True or False sin( )+sin=0 for any value of .Ch. 7.4 - True or False In establishing an identity, it is...Ch. 7.4 - Which of the following equation is not an...Ch. 7.4 - Which of the following equation is not an...Ch. 7.4 - The expression 1 1sin + 1 1+sin simplifies to...Ch. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - Prob. 15AYUCh. 7.4 - Prob. 16AYUCh. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - In Problems 11-20, simplify each trigonometric...Ch. 7.4 - establish each identity. secsin=tanCh. 7.4 - establish each identity. secsin=tanCh. 7.4 - establish each identity. 1+ tan 2 ( )= sec 2Ch. 7.4 - establish each identity. 1+ cot 2 ( )= csc 2Ch. 7.4 - establish each identity. cos( tan+cot )=cscCh. 7.4 - establish each identity. sin( cot+tan )=secCh. 7.4 - establish each identity. tanucotu cos 2 u= sin 2 uCh. 7.4 - establish each identity. sinucscu cos 2 u= sin 2 uCh. 7.4 - establish each identity. ( sec1 )( sec+1 )= tan 2Ch. 7.4 - establish each identity. ( csc1 )( csc+1 )= cot 2Ch. 7.4 - establish each identity. ( sec+tan )( sectan )=1Ch. 7.4 - establish each identity. ( csc+cot )( csccot )=1Ch. 7.4 - establish each identity. cos 2 ( 1+ tan 2 )=1Ch. 7.4 - Prob. 34AYUCh. 7.4 - establish each identity. ( sin+cos ) 2 + ( sincos...Ch. 7.4 - establish each identity. tan 2 cos 2 + cot 2 sin...Ch. 7.4 - establish each identity. sec 4 sec 2 = tan 4 +...Ch. 7.4 - establish each identity. csc 4 csc 2 = cot 4 +...Ch. 7.4 - establish each identity. secutanu= cosu 1+sinuCh. 7.4 - establish each identity. cscucotu= sinu 1+cosuCh. 7.4 - establish each identity. 3 sin 2 +4 cos 2 =3+ cos...Ch. 7.4 - establish each identity. 9 sec 2 5 tan 2 =5+4 sec...Ch. 7.4 - establish each identity. 1 cos 2 1+sin =sinCh. 7.4 - establish each identity. 1 sin 2 1cos =cosCh. 7.4 - In Problems establish each identity.
Ch. 7.4 - Prob. 46AYUCh. 7.4 - establish each identity. sec csc + sin cos =2tanCh. 7.4 - establish each identity. csc1 cot = cot csc+1Ch. 7.4 - establish each identity. 1+sin 1sin = csc+1 csc1Ch. 7.4 - establish each identity. cos+1 cos1 = 1+sec 1secCh. 7.4 - establish each identity. 1sin cos + cos 1sin =2secCh. 7.4 - establish each identity. cos 1+sin + 1+sin cos...Ch. 7.4 - establish each identity. sin sincos = 1 1cotCh. 7.4 - establish each identity. 1 sin 2 1+cos =cosCh. 7.4 - establish each identity. 1sin 1+sin = ( sectan ) 2Ch. 7.4 - Prob. 56AYUCh. 7.4 - establish each identity. cos 1tan + sin 1cot...Ch. 7.4 - establish each identity. cot 1tan + tan 1cot...Ch. 7.4 - establish each identity. tan+ cos 1+sin =secCh. 7.4 - establish each identity. tan+ cos 1+sin =secCh. 7.4 - establish each identity. tan+sec1 tansec+1...Ch. 7.4 - establish each identity. sincos+1 sin+cos1 = sin+1...Ch. 7.4 - establish each identity. tancot tan+cot = sin 2 ...Ch. 7.4 - Prob. 64AYUCh. 7.4 - establish each identity. tanucotu tanu+cotu +1=2...Ch. 7.4 - Prob. 66AYUCh. 7.4 - Prob. 67AYUCh. 7.4 - Prob. 68AYUCh. 7.4 - establish each identity. 1 tan 2 1+ tan 2 +1=2...Ch. 7.4 - establish each identity. 1 cot 2 1+ cot 2 +2 cos...Ch. 7.4 - establish each identity. seccsc seccsc =sincosCh. 7.4 - establish each identity. sin 2 tan cos 2 cot = tan...Ch. 7.4 - establish each identity. seccos=sintanCh. 7.4 - establish each identity. tan+cot=seccscCh. 7.4 - establish each identity. 1 1sin + 1 1+sin =2 sec 2Ch. 7.4 - establish each identity. 1+sin 1sin 1sin 1+sin...Ch. 7.4 - establish each identity. sec 1sin = 1+sin cos 3Ch. 7.4 - Prob. 78AYUCh. 7.4 - Prob. 79AYUCh. 7.4 - establish each identity. sec 2 tan 2 +tan sec...Ch. 7.4 - establish each identity. sin+cos cos sincos sin...Ch. 7.4 - Prob. 82AYUCh. 7.4 - Prob. 83AYUCh. 7.4 - establish each identity. sin 3 +co s 3 12 cos 2 ...Ch. 7.4 - establish each identity. co s 2 sin 2 1 tan 2 =...Ch. 7.4 - Prob. 86AYUCh. 7.4 - Prob. 87AYUCh. 7.4 - establish each identity. 12 cos 2 sincos =tancotCh. 7.4 - establish each identity. 1+sin+cos 1+sincos =...Ch. 7.4 - Prob. 90AYUCh. 7.4 - Prob. 91AYUCh. 7.4 - establish each identity. ( 2asincos ) 2 + a 2 (...Ch. 7.4 - establish each identity. tan+tan cot+cot =tantanCh. 7.4 - establish each identity. ( tan+tan )( 1cotcot )+(...Ch. 7.4 - Prob. 95AYUCh. 7.4 - Prob. 96AYUCh. 7.4 - establish each identity. ln| sec |=ln| cos |Ch. 7.4 - Prob. 98AYUCh. 7.4 - Prob. 99AYUCh. 7.4 - Prob. 100AYUCh. 7.4 - In Problems 101-104, show that the functions f and...Ch. 7.4 - Prob. 102AYUCh. 7.4 - Prob. 103AYUCh. 7.4 - Prob. 104AYUCh. 7.4 - Searchlights A searchlight at the grand opening of...Ch. 7.4 - Optical Measurement Optical methods of measurement...Ch. 7.4 - Prob. 107AYUCh. 7.4 - Prob. 108AYUCh. 7.4 - Prob. 109AYUCh. 7.4 - Prob. 110AYUCh. 7.4 - Prob. 111AYUCh. 7.4 - Prob. 112AYUCh. 7.4 - Prob. 113AYUCh. 7.4 - Prob. 114AYUCh. 7.5 - The distance d from the point ( 2,3 ) to the point...Ch. 7.5 - If sin= 4 5 and is in quadrant II, then cos=...Ch. 7.5 - (a) sin 4 cos 3 = _____ . (pp. 382-385) (b) tan ...Ch. 7.5 - If sin= 4 5 , 3 2 then cos= ____ . (pp.401-403)Ch. 7.5 - Prob. 5AYUCh. 7.5 - Prob. 6AYUCh. 7.5 - True or False sin( + )=sin+sin+2sinsinCh. 7.5 - Prob. 8AYUCh. 7.5 - True or False cos( 2 )=cosCh. 7.5 - True or False If f( x )=sinxandg( x )=cosx , then...Ch. 7.5 - Choose the expression that completes the sum...Ch. 7.5 - Choose the expression that is equivalent to sin 60...Ch. 7.5 - Find the exact value of each expression. cos 165Ch. 7.5 - Find the exact value of each expression. sin 105Ch. 7.5 - Find the exact value of each expression. tan 15Ch. 7.5 - Find the exact value of each expression. tan 195Ch. 7.5 - Find the exact value of each expression. sin 5 12Ch. 7.5 - Find the exact value of each expression. sin 12Ch. 7.5 - Find the exact value of each expression. cos 7 12Ch. 7.5 - Find the exact value of each expression. tan 7 12Ch. 7.5 - Find the exact value of each expression. sin 17 12Ch. 7.5 - Find the exact value of each expression. tan 19 12Ch. 7.5 - Find the exact value of each expression. sec( 12...Ch. 7.5 - Find the exact value of each expression. cot( 5...Ch. 7.5 - Find the exact value of each expression. sin 20 ...Ch. 7.5 - Find the exact value of each expression. sin 20 ...Ch. 7.5 - Find the exact value of each expression. cos 70 ...Ch. 7.5 - Find the exact value of each expression. cos 40 ...Ch. 7.5 - Find the exact value of each expression. tan 20 ...Ch. 7.5 - Find the exact value of each expression. tan 40 ...Ch. 7.5 - Find the exact value of each expression. sin 12...Ch. 7.5 - Find the exact value of each expression. cos 5 12...Ch. 7.5 - Find the exact value of each expression. cos 12...Ch. 7.5 - Find the exact value of each expression. sin 18...Ch. 7.5 - In Problems 35-40, find the exact value of each of...Ch. 7.5 - In Problems 35-40, find the exact value of each of...Ch. 7.5 - In Problems 35-40, find the exact value of each of...Ch. 7.5 - In Problems 35-40, find the exact value of each of...Ch. 7.5 - In Problems 35-40, find the exact value of each of...Ch. 7.5 - In Problems 35-40, find the exact value of each of...Ch. 7.5 - If sin= 1 3 , in quadrant II, find the exact value...Ch. 7.5 - If cos= 1 4 , in quadrant IV, find the exact value...Ch. 7.5 - In problems 43-48, use the figures to evaluate...Ch. 7.5 - In problems 43-48, use the figures to evaluate...Ch. 7.5 - In problems 43-48, use the figures to evaluate...Ch. 7.5 - In problems 43-48, use the figures to evaluate...Ch. 7.5 - Prob. 47AYUCh. 7.5 - In problems 43-48, use the figures to evaluate...Ch. 7.5 - establish each identify. sin( 2 + )=cosCh. 7.5 - establish each identify. cos( 2 + )=sinCh. 7.5 - Prob. 51AYUCh. 7.5 - Prob. 52AYUCh. 7.5 - establish each identify. sin( + )=sinCh. 7.5 - Prob. 54AYUCh. 7.5 - establish each identify. tan( )=tanCh. 7.5 - establish each identify. tan( 2 )=tanCh. 7.5 - Prob. 57AYUCh. 7.5 - Prob. 58AYUCh. 7.5 - Prob. 59AYUCh. 7.5 - establish each identify. cos( + )+cos( )=2coscosCh. 7.5 - Prob. 61AYUCh. 7.5 - establish each identify. sin( + ) coscos =tan+tanCh. 7.5 - establish each identify. cos( + ) coscos =1tantanCh. 7.5 - establish each identify. cos( ) sincos =cot+tanCh. 7.5 - establish each identify. sin( + ) sin( ) =...Ch. 7.5 - establish each identify. cos( + ) cos( ) =...Ch. 7.5 - establish each identify. cot( + )= cotcot1 cot+cotCh. 7.5 - establish each identify. cot( )= cotcot+1 cotcotCh. 7.5 - establish each identify. sec( + )= csccsc cotcot1Ch. 7.5 - establish each identify. sec( )= secsec 1+tantanCh. 7.5 - establish each identify. sin( )sin( + )= sin 2 ...Ch. 7.5 - establish each identify. cos( )cos( + )= cos 2 ...Ch. 7.5 - establish each identify. sin( +k )= ( 1 ) k sin,k...Ch. 7.5 - establish each identify. cos( +k )= ( 1 ) k cos,k...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In Problems find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In problems 75-86, find the exact value of each...Ch. 7.5 - In Problems 87-92, write each trigonometric...Ch. 7.5 - In Problems 87-92, write each trigonometric...Ch. 7.5 - In Problems 87-92, write each trigonometric...Ch. 7.5 - In Problems 87-92, write each trigonometric...Ch. 7.5 - In Problems 87-92, write each trigonometric...Ch. 7.5 - In Problems 87-92, write each trigonometric...Ch. 7.5 - In problems 93-98, solve each equation on the...Ch. 7.5 - In problems 93-98, solve each equation on the...Ch. 7.5 - In problems 93-98, solve each equation on the...Ch. 7.5 - In problems 93-98, solve each equation on the...Ch. 7.5 - In problems 93-98, solve each equation on the...Ch. 7.5 - In problems 93-98, solve each equation on the...Ch. 7.5 -
Ch. 7.5 - Show that tan1+cot1=2.Ch. 7.5 - Show that tan1(1)=2tan1, if 0.Ch. 7.5 - Show that if
Ch. 7.5 - Show that sin( sin 1 v+ cos 1 v )=1 .Ch. 7.5 - Show that cos( sin 1 v+ cos 1 v )=0 .Ch. 7.5 - Calculus Show that the difference quotient for f(...Ch. 7.5 - Calculus Show that the difference quotient for f(...Ch. 7.5 - One, Two, Three (a) Show that tan( tan 1 1+ tan 1...Ch. 7.5 - Electric Power In an alternating current (ac)...Ch. 7.5 - Prob. 109AYUCh. 7.5 - If ++= 180 andcot=cot+cot+cot0 90 show that sin...Ch. 7.5 - If tan=x+1andtan=x1 , show that 2cot( )= x 2Ch. 7.5 - Discuss the following derivation: tan( + 2 )=...Ch. 7.5 - Explain why formula (7) cannot be used to show...Ch. 7.5 - Determine the points of intersection of the graphs...Ch. 7.5 - Convert 17 6 to degrees.Ch. 7.5 - Problems are based on material learned earlier in...Ch. 7.5 - Problems 114117 are based on material learned...Ch. 7.6 - cos( 2 )= cos 2 =1=1Ch. 7.6 - Prob. 2AYUCh. 7.6 - tan 2 = 1cosCh. 7.6 - True or False tan( 20 )= 2tan 1 tan 2Ch. 7.6 - True or False sin( 2 ) has two equivalent forms:...Ch. 7.6 - True or False tan( 2 )+tan( 2 )=tan( 4 )Ch. 7.6 - Choose the expression that completes the...Ch. 7.6 - If sin= 1cos 2 , then which of the following...Ch. 7.6 - In Problems use the information given about the...Ch. 7.6 - In Problems 920, use the information given about...Ch. 7.6 - In Problems use the information given about the...Ch. 7.6 - In Problems 920, use the information given about...Ch. 7.6 - In Problems 920, use the information given about...Ch. 7.6 - In Problems 920, use the information given about...Ch. 7.6 - In Problems use the information given about the...Ch. 7.6 - In Problems use the information given about the...Ch. 7.6 - In Problems use the information given about the...Ch. 7.6 - In Problems 920, use the information given about...Ch. 7.6 - In Problems 920, use the information given about...Ch. 7.6 - In Problems use the information given about the...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 21-30, use the Half-angle Formulas to...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - In Problems 31-42, use the figures to evaluate...Ch. 7.6 - Show that sin 4 = 3 8 1 2 cos( 2 )+ 1 8 cos( 4 )Ch. 7.6 - Show that sin( 4 )=( cos )( 4sin8 sin 3 ) .Ch. 7.6 - Develop a formula for cos( 3 ) as a third-degree...Ch. 7.6 - Prob. 46AYUCh. 7.6 - Prob. 47AYUCh. 7.6 - Find an expression for cos( 5 ) as a fifth-degree...Ch. 7.6 - cos 4 sin 4 =cos( 2 )Ch. 7.6 - Prob. 50AYUCh. 7.6 - establish each identify. cot( 2 )= cot 2 -1 2cotCh. 7.6 - establish each identify. cot( 2 )= 1 2 ( cot-tan )Ch. 7.6 - establish each identify. sec( 2 )= sec 2 2- sec 2Ch. 7.6 - Prob. 54AYUCh. 7.6 - establish each identify. cos 2 ( 2u ) -sin 2 ( 2u...Ch. 7.6 - Prob. 56AYUCh. 7.6 - establish each identify. cos( 2 ) 1+sin( 2 ) =...Ch. 7.6 - Prob. 58AYUCh. 7.6 - Prob. 59AYUCh. 7.6 - Prob. 60AYUCh. 7.6 - establish each identify. cot 2 v 2 = secv+1 secv-1Ch. 7.6 - Prob. 62AYUCh. 7.6 - Prob. 63AYUCh. 7.6 - establish each identify. 1- 1 2 sin( 2 )= sin 3 ...Ch. 7.6 - Prob. 65AYUCh. 7.6 - Prob. 66AYUCh. 7.6 - establish each identify. tan( 3 )= 3tan tan 3 13...Ch. 7.6 - Prob. 68AYUCh. 7.6 - Prob. 69AYUCh. 7.6 - Prob. 70AYUCh. 7.6 - solve each equation on the interval 02 . cos( 2...Ch. 7.6 - solve each equation on the interval 02 . cos( 2...Ch. 7.6 - solve each equation on the interval 02 . cos( 2...Ch. 7.6 - solve each equation on the interval 02 . sin( 2...Ch. 7.6 - Prob. 75AYUCh. 7.6 - solve each equation on the interval 02 . cos( 2...Ch. 7.6 - Prob. 77AYUCh. 7.6 - solve each equation on the interval 02 . cos( 2...Ch. 7.6 - Prob. 79AYUCh. 7.6 - solve each equation on the interval 02 . tan( 2...Ch. 7.6 - find the exact value of each expression. sin( 2...Ch. 7.6 - find the exact value of each expression. sin[ 2...Ch. 7.6 - find the exact value of each expression. cos( 2...Ch. 7.6 - find the exact value of each expression. cos( 2...Ch. 7.6 - find the exact value of each expression. tan[ 2...Ch. 7.6 - find the exact value of each expression. tan( 2...Ch. 7.6 - Prob. 87AYUCh. 7.6 - find the exact value of each expression. cos[ 2...Ch. 7.6 - Prob. 89AYUCh. 7.6 - find the exact value of each expression. cos 2 ( 1...Ch. 7.6 - Prob. 91AYUCh. 7.6 - find the exact value of each expression. csc[ 2...Ch. 7.6 - Prob. 93AYUCh. 7.6 - find the real zeros of each trigonometric function...Ch. 7.6 - Prob. 95AYUCh. 7.6 - Constructing a Rain Gutter A rain gutter is to be...Ch. 7.6 - Laser Projection In a laser projection system, the...Ch. 7.6 - Prob. 98AYUCh. 7.6 - Projectile Motion An object is propelled upward at...Ch. 7.6 - Prob. 100AYUCh. 7.6 - Prob. 101AYUCh. 7.6 - Geometry A rectangle is inscribed in a semicircle...Ch. 7.6 - Prob. 103AYUCh. 7.6 - Prob. 104AYUCh. 7.6 - Prob. 105AYUCh. 7.6 - Prob. 106AYUCh. 7.6 - If z=tan 2 , show that sin= 2z 1+ z 2 .Ch. 7.6 - Prob. 108AYUCh. 7.6 - Prob. 109AYUCh. 7.6 - Prob. 110AYUCh. 7.6 - Prob. 111AYUCh. 7.6 - Prob. 112AYUCh. 7.6 - Prob. 113AYUCh. 7.6 - Prob. 114AYUCh. 7.6 - Prob. 115AYUCh. 7.6 - Prob. 117AYUCh. 7.6 - Prob. 118AYUCh. 7.6 - Find the exact value of sin( 2 3 )cos( 4 3 ) .Ch. 7.6 - Prob. 120AYUCh. 7.7 - find the exact value of each expression. sin 195 ...Ch. 7.7 - find the exact value of each expression. cos 285 ...Ch. 7.7 - find the exact value of each expression. sin 195 ...Ch. 7.7 - find the exact value of each expression. sin 75 ...Ch. 7.7 - Find the exact value of each expression. cos 225 ...Ch. 7.7 - Find the exact value of each expression. sin 255 ...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each product as a sum containing only...Ch. 7.7 - express each sum or difference as a product of...Ch. 7.7 - express each sum or difference as a product of...Ch. 7.7 - express each sum or difference as a product of...Ch. 7.7 - Prob. 20AYUCh. 7.7 - express each sum or difference as a product of...Ch. 7.7 - Prob. 22AYUCh. 7.7 - Prob. 23AYUCh. 7.7 - express each sum or difference as a product of...Ch. 7.7 - establish each identify. sin+sin(3) 2sin(2) =cosCh. 7.7 - establish each identify. cos+cos(3) 2cos(2) =cosCh. 7.7 - establish each identify. sin(4)+sin(2)...Ch. 7.7 - Prob. 28AYUCh. 7.7 - establish each identify. cos-cos(3) sin+sin(3)...Ch. 7.7 - Prob. 30AYUCh. 7.7 - Prob. 31AYUCh. 7.7 - Prob. 32AYUCh. 7.7 - Prob. 33AYUCh. 7.7 - Prob. 34AYUCh. 7.7 - Prob. 35AYUCh. 7.7 - Prob. 36AYUCh. 7.7 - Prob. 37AYUCh. 7.7 - Prob. 38AYUCh. 7.7 - Prob. 39AYUCh. 7.7 - Prob. 40AYUCh. 7.7 - Prob. 41AYUCh. 7.7 - establish each identify. 1-cos( 2 )+cos( 4 )-cos(...Ch. 7.7 - Prob. 43AYUCh. 7.7 - solve each equation on the interval 02 cos( 2...Ch. 7.7 - Prob. 45AYUCh. 7.7 - solve each equation on the interval 02 sin( 4...Ch. 7.7 - Prob. 51AYUCh. 7.7 - Prob. 53AYUCh. 7.7 - Prob. 54AYUCh. 7.7 - Prob. 55AYUCh. 7.7 - Prob. 56AYUCh. 7.7 - Prob. 57AYUCh. 7.7 - Prob. 58AYUCh. 7.7 - Prob. 59AYUCh. 7.7 - Prob. 60AYUCh. 7 - In problems 714, find the exact value of each...Ch. 7 - In problems 714, find the exact value of each...Ch. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - Find the exact value, if any, of each composite...Ch. 7 - In Problems, find the exact value, if any, of each...Ch. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - In Problems 26 and 27, write each trigonometric...Ch. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - In Problems 28-44, establish each identity. sin 2...Ch. 7 - In Problems 28-44, establish each identity. 5 cos...Ch. 7 - In Problems 28-44, establish each identity. 1cos...Ch. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - In Problems 28-44, establish each identity....Ch. 7 - In Problems 28-44, establish each identity. 1sin...Ch. 7 - In Problems 28-44, establish each identity. 12sin...Ch. 7 - In Problems 28-44, establish each identity. cos( +...Ch. 7 - In Problems 28-44, establish each identity. cos( ...Ch. 7 - In Problems 28-44, establish each identity. (...Ch. 7 - In Problems 28-44, establish each identity....Ch. 7 - In Problems 28-44, establish each identity. 18 sin...Ch. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - In Problems 45-52, find the exact value of each...Ch. 7 - Prob. 50RECh. 7 - In Problems 45-52, find the exact value of each...Ch. 7 - Prob. 52RECh. 7 - Prob. 53RECh. 7 - Prob. 54RECh. 7 - In Problems, Use the information given about the...Ch. 7 - In Problems 5357, Use the information given about...Ch. 7 - Prob. 57RECh. 7 - In Problems 58-63, find the exact value of each...Ch. 7 - In Problems 58-63, find the exact value of each...Ch. 7 - In Problems 58-63, find the exact value of each...Ch. 7 - In Problems 58-63, find the exact value of each...Ch. 7 - In Problems 58-63, find the exact value of each...Ch. 7 - In Problems 58-63, find the exact value of each...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 64-75, solve each equation on the...Ch. 7 - In Problems 76 - 80, use a calculator to find an...Ch. 7 - In Problems 76 - 80, use a calculator to find an...Ch. 7 - In Problems 76 - 80, use a calculator to find an...Ch. 7 - Prob. 79RECh. 7 - Prob. 80RECh. 7 - In Problems 81-83, use a graphing utility to solve...Ch. 7 - In Problems 81-83, use a graphing utility to solve...Ch. 7 - In Problems 81-83, use a graphing utility to solve...Ch. 7 - In Problems 84 and 85, find the exact solution of...Ch. 7 - In Problems 84 and 85, find the exact solution of...Ch. 7 - Use a Half-angle Formula to find the exact value...Ch. 7 - If you are given the value of cos and want the...Ch. 7 - Prob. 1CTCh. 7 - In problems 110, find the exact value of each...Ch. 7 - Prob. 3CTCh. 7 - Prob. 4CTCh. 7 - Prob. 5CTCh. 7 - Prob. 6CTCh. 7 - Prob. 7CTCh. 7 - Prob. 8CTCh. 7 - Prob. 9CTCh. 7 - Prob. 10CTCh. 7 - Prob. 11CTCh. 7 - Prob. 12CTCh. 7 - Prob. 13CTCh. 7 - In problems establish each identity.
Ch. 7 - Prob. 15CTCh. 7 - Prob. 16CTCh. 7 - In problems 2128, use sum, difference, product, or...Ch. 7 - Prob. 18CTCh. 7 - Prob. 19CTCh. 7 - Prob. 20CTCh. 7 - Prob. 21CTCh. 7 - Prob. 22CTCh. 7 - In problems 2128, use sum, difference, product, or...Ch. 7 - Prob. 24CTCh. 7 - Prob. 25CTCh. 7 - Prob. 26CTCh. 7 - Prob. 27CTCh. 7 - Prob. 28CTCh. 7 - Prob. 29CTCh. 7 - Find the real solutions, if any of the equation...Ch. 7 - Find the equation for the line containing the...Ch. 7 - Prob. 3CRCh. 7 - Prob. 4CRCh. 7 - Prob. 5CRCh. 7 - Prob. 6CRCh. 7 - Prob. 7CRCh. 7 - Prob. 8CRCh. 7 - Prob. 9CRCh. 7 - Prob. 10CRCh. 7 - Consider the function f(x)=2x5x44x3+2x2+2x1 Find...Ch. 7 - Prob. 12CR
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- (7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.arrow_forward(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward
- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
- (8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward
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