Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
Question
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Chapter 6.6, Problem 39AYU
To determine

To find: Explain how the amplitude and period of a sinusoidal graph are used to establish the scale on each coordinate axis:

Expert Solution
Check Mark

Answer to Problem 39AYU

Solution:

Sinusoidal functions produce graphs that look like waves, and any portion of the curve can be translated onto another portion of the curve. Circular motion and pendulum movement are excellent “real life” examples of sinusoidal relationships.

A sinusoidal function is a function that is like a sine function in the sense that the function can be produced by shifting, stretching or compressing the sine function.

You can graph sinusoidal functions using your knowledge of transformations.

There are 5 transformations that can affect trig functions:

  • horizontal stretch (HS) alters the period
  • vertical stretch (VS) alters the amplitude
  • horizontal translation (HT) causes a phase shift relocating our initial point
  • vertical translation (VT) relocates the sinusoidal axis
  • reflection (± )changes the pattern of our 5 key points

Precalculus Enhanced with Graphing Utilities, Chapter 6.6, Problem 39AYU , additional homework tip  1

Explanation of Solution

Sinusoidal functions produce graphs that look like waves, and any portion of the curve can be translated onto another portion of the curve. Circular motion and pendulum movement are excellent “real life” examples of sinusoidal relationships.

A sinusoidal function is a function that is like a sine function in the sense that the function can be produced by shifting, stretching or compressing the sine function.

You can graph sinusoidal functions using your knowledge of transformations.

There are 5 transformations that can affect trig functions:

  • horizontal stretch (HS) alters the period
  • vertical stretch (VS) alters the amplitude
  • horizontal translation (HT) causes a phase shift relocating our initial point
  • vertical translation (VT) relocates the sinusoidal axis
  • reflection (± )changes the pattern of our 5 key points

Precalculus Enhanced with Graphing Utilities, Chapter 6.6, Problem 39AYU , additional homework tip  2

Some basic vocabulary should be observed as shown in the diagram:

Period: a complete cycle of the graph where the graph starts to repeat.

Sinusoidal axis: horizontal line halfway between the local maximum and minimum.

Amplitude: vertical distance from the sinusoidal axis to the maximum or minimum

Local maximum: the tops of each “wave”, all equal in value

Local minimum: the bottoms of each “wave”, all equal in value

The relations involving sine or cosine can be expressed in the form:

1 A (y  D) = sinB(x  C)or 1 A (y  D) = cosB(x  C)

  • Determine the position of the sinusoidal axis.

    Sinusoidal axis =  max + min 2

    This is the Vertical Translation or “D” in the formula.

  • Determine the amplitude of the function.

    Amplitude = max – sinusoidal axis

    This is the Vertical Stretch or “A” in the formula.

  • Determine the period of the graph for the function.

    Horizontal Stretch =  period 360º

    This is the Horizontal Stretch or “B” in the formula.

  • Determine the phase shift.

    Phase Shift = x  coordinate of maximum

    This is the Horizontal Translation or “C” in the formula.

Graphing a Sinusoidal Function

The procedure for graphing sinusoidal functions is similar to quadratic functions.

y = Asin( ωx  ϕ ) + B or y = Acos( ωx  ϕ ) + B

Here A is the amplitude function. We know the maximum and minimum value of sine and cosine is ±1 . Therefore y-axis takes value from A to A .

Both sine and cosine have the domain is ( ,  ) .

Therefore x-axis takes values are ( ,  ) .

Chapter 6 Solutions

Precalculus Enhanced with Graphing Utilities

Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 11-22, draw each angle in standard...Ch. 6.1 - In Problems 59-64, convert each angle to a decimal...Ch. 6.1 - In Problems 59-64, convert each angle to a decimal...Ch. 6.1 - Prob. 25AYUCh. 6.1 - Prob. 26AYUCh. 6.1 - In Problems 59-64, convert each angle to a decimal...Ch. 6.1 - Prob. 28AYUCh. 6.1 - In Problems 65-70, convert each angle to DMS form....Ch. 6.1 - In Problems 65-70, convert each angle to DMS form....Ch. 6.1 - In Problems 65-70, convert each angle to DMS form....Ch. 6.1 - In Problems 65-70, convert each angle to DMS form....Ch. 6.1 - In Problems 65-70, convert each angle to DMS form....Ch. 6.1 - In Problems 65-70, convert each angle to DMS form....Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 23-34, convert each angle in degrees...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 35—46, convert each angle in radians...Ch. 6.1 - In Problems 47-52, convert each angle in degrees...Ch. 6.1 - In Problems 47-52, convert each angle in degrees...Ch. 6.1 - In Problems 47-52, convert each angle in degrees...Ch. 6.1 - In Problems 47-52, convert each angle in degrees...Ch. 6.1 - In Problems 47-52, convert each angle in degrees...Ch. 6.1 - In Problems 47-52, convert each angle in degrees...Ch. 6.1 - In Problems 53-58, convert each angle in radians...Ch. 6.1 - In Problems 53-58, convert each angle in radians...Ch. 6.1 - In Problems 53-58, convert each angle in radians...Ch. 6.1 - In Problems 53-58, convert each angle in radians...Ch. 6.1 - In Problems 53-58, convert each angle in radians...Ch. 6.1 - In Problems 53-58, convert each angle in radians...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 71-78, s denotes the length of the are...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - In Problems 79-86, A denotes the area of the...Ch. 6.1 - Prob. 87AYUCh. 6.1 - Prob. 88AYUCh. 6.1 - Prob. 89AYUCh. 6.1 - Prob. 90AYUCh. 6.1 - Prob. 91AYUCh. 6.1 - Prob. 92AYUCh. 6.1 - Prob. 93AYUCh. 6.1 - Prob. 94AYUCh. 6.1 - Prob. 95AYUCh. 6.1 - Prob. 96AYUCh. 6.1 - Prob. 97AYUCh. 6.1 - Prob. 98AYUCh. 6.1 - Prob. 99AYUCh. 6.1 - Prob. 100AYUCh. 6.1 - Prob. 101AYUCh. 6.1 - Prob. 102AYUCh. 6.1 - Prob. 103AYUCh. 6.1 - Prob. 104AYUCh. 6.1 - Prob. 105AYUCh. 6.1 - Prob. 106AYUCh. 6.1 - Prob. 107AYUCh. 6.1 - Prob. 108AYUCh. 6.1 - Prob. 109AYUCh. 6.1 - Prob. 110AYUCh. 6.1 - Prob. 111AYUCh. 6.1 - Prob. 112AYUCh. 6.1 - Prob. 113AYUCh. 6.1 - Prob. 114AYUCh. 6.1 - Prob. 115AYUCh. 6.1 - Prob. 116AYUCh. 6.1 - Prob. 117AYUCh. 6.1 - Prob. 118AYUCh. 6.1 - Prob. 119AYUCh. 6.1 - Prob. 120AYUCh. 6.1 - Prob. 121AYUCh. 6.1 - Prob. 122AYUCh. 6.1 - Prob. 123AYUCh. 6.1 - Prob. 124AYUCh. 6.1 - Prob. 125AYUCh. 6.2 - Prob. 1AYUCh. 6.2 - Prob. 2AYUCh. 6.2 - Prob. 3AYUCh. 6.2 - Prob. 4AYUCh. 6.2 - Prob. 5AYUCh. 6.2 - Prob. 6AYUCh. 6.2 - Prob. 7AYUCh. 6.2 - Prob. 8AYUCh. 6.2 - Prob. 9AYUCh. 6.2 - Prob. 10AYUCh. 6.2 - Prob. 11AYUCh. 6.2 - Prob. 12AYUCh. 6.2 - Prob. 13AYUCh. 6.2 - Prob. 14AYUCh. 6.2 - Prob. 15AYUCh. 6.2 - Prob. 16AYUCh. 6.2 - Prob. 17AYUCh. 6.2 - Prob. 18AYUCh. 6.2 - Prob. 19AYUCh. 6.2 - Prob. 20AYUCh. 6.2 - Prob. 21AYUCh. 6.2 - Prob. 22AYUCh. 6.2 - Prob. 23AYUCh. 6.2 - Prob. 24AYUCh. 6.2 - Prob. 25AYUCh. 6.2 - Prob. 26AYUCh. 6.2 - Prob. 27AYUCh. 6.2 - Prob. 28AYUCh. 6.2 - Prob. 29AYUCh. 6.2 - Prob. 30AYUCh. 6.2 - Prob. 31AYUCh. 6.2 - Prob. 32AYUCh. 6.2 - Prob. 33AYUCh. 6.2 - Prob. 34AYUCh. 6.2 - Prob. 35AYUCh. 6.2 - Prob. 36AYUCh. 6.2 - Prob. 37AYUCh. 6.2 - Prob. 38AYUCh. 6.2 - Prob. 39AYUCh. 6.2 - Prob. 40AYUCh. 6.2 - 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Prob. 135AYUCh. 6.3 - The domain of the function f(x)= x+1 2x+1 is _____...Ch. 6.3 - A function for which f(x)=f(x) for all x in the...Ch. 6.3 - True or False The function f(x)= x is even....Ch. 6.3 - True or False The equation x 2 +2x= (x+1) 2 1 is...Ch. 6.3 - The sine, cosine, cosecant, and secant functions...Ch. 6.3 - The domain of the tangent function is _____ .Ch. 6.3 - Which of the following is not in the range of the...Ch. 6.3 - Which of the following functions is even? a....Ch. 6.3 - sin 2 + cos 2 = _____ .Ch. 6.3 - True or False sec= 1 sinCh. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - ln Problems 11-26, use the fact that the...Ch. 6.3 - In Problems 27—34, name the quadrant in which...Ch. 6.3 - In Problems 27—34, name the quadrant in which...Ch. 6.3 - In Problems 27—34, name the quadrant in which...Ch. 6.3 - In Problems 27—34, name the quadrant in which...Ch. 6.3 - In Problems 27—34, name the quadrant in which...Ch. 6.3 - In Problems 27—34, name the quadrant in which...Ch. 6.3 - In Problems 27—34, name the quadrant in which...Ch. 6.3 - Prob. 34AYUCh. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In problems 35-42, sin and cos are given. Find the...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 43-58, find the exact value of each of...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 59-76, use the even-odd properties to...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - In Problems 77-88, use properties of the...Ch. 6.3 - If sin=0.3 , find the value of: sin+sin( +2 )+sin(...Ch. 6.3 - If cos=0.2 , find the value of: cos+cos( +2 )+cos(...Ch. 6.3 - If tan=3 , find the value of: tan+tan( + )+tan( +2...Ch. 6.3 - If cot=2 , find the value of: cot+cot( - )+cot( -2...Ch. 6.3 - Find the exact value of: sin 1 + sin2 + sin3 ++...Ch. 6.3 - Find the exact value of: cos 1 + cos2 + cos3 ++...Ch. 6.3 - What is the domain of the sine function?Ch. 6.3 - What is the domain of the cosine function?Ch. 6.3 - For what numbers is f( )=tan not defined?Ch. 6.3 - For what numbers is f( )=cot not defined?Ch. 6.3 - For what numbers is f( )=sec not defined?Ch. 6.3 - For what numbers is f( )=csc not defined?Ch. 6.3 - What is the range of the sine function?Ch. 6.3 - What is the range of the cosine function?Ch. 6.3 - What is the range of the tangent function?Ch. 6.3 - What is the range of the cotangent function?Ch. 6.3 - What is the range of the secant function?Ch. 6.3 - What is the range of the cosecant function?Ch. 6.3 - Is the sine function even, odd, or neither? Is its...Ch. 6.3 - Is the cosine function even, odd, or neither? Is...Ch. 6.3 - Is the tangent function even, odd, or neither? Is...Ch. 6.3 - Is the cotangent function even, odd, or neither?...Ch. 6.3 - Is the cotangent function even, odd, or neither?...Ch. 6.3 - Is the cotangent function even, odd, or neither?...Ch. 6.3 - In Problems 113-118, use the periodic and even-odd...Ch. 6.3 - In Problems 113-118, use the periodic and even-odd...Ch. 6.3 - In Problems 113-118, use the periodic and even-odd...Ch. 6.3 - In Problems 113-118, use the periodic and even-odd...Ch. 6.3 - In Problems 113-118, use the periodic and even-odd...Ch. 6.3 - In Problems 113-118, use the periodic and even-odd...Ch. 6.3 - Calculating the Time of a Trip From a parking lot,...Ch. 6.3 - Calculating the Time of a Trip Two oceanfront...Ch. 6.3 - Show that the range of the tangent function is the...Ch. 6.3 - Show that the range of the cotangent function is...Ch. 6.3 - Show that the period of f( )=sin is 2 . [Hint:...Ch. 6.3 - show that the period of f( )=cos is 2 .Ch. 6.3 - show that the period of f( )=sec is 2 .Ch. 6.3 - show that the period of f( )=csc is 2 .Ch. 6.3 - show that the period of f( )=tan is .Ch. 6.3 - show that the period of f( )=cot is .Ch. 6.3 - Prove the reciprocal identities given in formula...Ch. 6.3 - Prove the quotient identities given in formula...Ch. 6.3 - Establish the identity: (sincos) 2 + (sinsin) 2 +...Ch. 6.3 - Write down five properties of the tangent...Ch. 6.3 - Describe your understanding of the meaning of a...Ch. 6.3 - Explain how to find the value of sin 390 using...Ch. 6.3 - Explain how to find the value of cos( 45 ) using...Ch. 6.3 - Explain how to find the value of sin 390 and cos(...Ch. 6.4 - Prob. 1AYUCh. 6.4 - Prob. 2AYUCh. 6.4 - Prob. 3AYUCh. 6.4 - Prob. 4AYUCh. 6.4 - Prob. 5AYUCh. 6.4 - Prob. 6AYUCh. 6.4 - Prob. 7AYUCh. 6.4 - Prob. 8AYUCh. 6.4 - Prob. 9AYUCh. 6.4 - Prob. 10AYUCh. 6.4 - Prob. 11AYUCh. 6.4 - Prob. 12AYUCh. 6.4 - Prob. 13AYUCh. 6.4 - Prob. 14AYUCh. 6.4 - Prob. 15AYUCh. 6.4 - Prob. 16AYUCh. 6.4 - Prob. 17AYUCh. 6.4 - Prob. 18AYUCh. 6.4 - Prob. 19AYUCh. 6.4 - Prob. 20AYUCh. 6.4 - Prob. 21AYUCh. 6.4 - Prob. 22AYUCh. 6.4 - Prob. 23AYUCh. 6.4 - Prob. 24AYUCh. 6.4 - Prob. 25AYUCh. 6.4 - Prob. 26AYUCh. 6.4 - Prob. 27AYUCh. 6.4 - Prob. 28AYUCh. 6.4 - Prob. 29AYUCh. 6.4 - Prob. 30AYUCh. 6.4 - Prob. 31AYUCh. 6.4 - Prob. 32AYUCh. 6.4 - Prob. 33AYUCh. 6.4 - Prob. 34AYUCh. 6.4 - Prob. 35AYUCh. 6.4 - Prob. 36AYUCh. 6.4 - Prob. 37AYUCh. 6.4 - Prob. 38AYUCh. 6.4 - Prob. 39AYUCh. 6.4 - Prob. 40AYUCh. 6.4 - Prob. 41AYUCh. 6.4 - Prob. 42AYUCh. 6.4 - Prob. 43AYUCh. 6.4 - Prob. 44AYUCh. 6.4 - Prob. 45AYUCh. 6.4 - Prob. 46AYUCh. 6.4 - Prob. 47AYUCh. 6.4 - Prob. 48AYUCh. 6.4 - Prob. 49AYUCh. 6.4 - Prob. 50AYUCh. 6.4 - Prob. 51AYUCh. 6.4 - Prob. 52AYUCh. 6.4 - Prob. 53AYUCh. 6.4 - Prob. 54AYUCh. 6.4 - Prob. 55AYUCh. 6.4 - Prob. 56AYUCh. 6.4 - Prob. 57AYUCh. 6.4 - Prob. 58AYUCh. 6.4 - Prob. 59AYUCh. 6.4 - Prob. 60AYUCh. 6.4 - Prob. 61AYUCh. 6.4 - Prob. 62AYUCh. 6.4 - Prob. 63AYUCh. 6.4 - Prob. 64AYUCh. 6.4 - Prob. 65AYUCh. 6.4 - Prob. 66AYUCh. 6.4 - Prob. 67AYUCh. 6.4 - Prob. 68AYUCh. 6.4 - Prob. 69AYUCh. 6.4 - Prob. 70AYUCh. 6.4 - Prob. 71AYUCh. 6.4 - Prob. 72AYUCh. 6.4 - Prob. 73AYUCh. 6.4 - Prob. 74AYUCh. 6.4 - Prob. 75AYUCh. 6.4 - Prob. 76AYUCh. 6.4 - Prob. 77AYUCh. 6.4 - Prob. 78AYUCh. 6.4 - Prob. 79AYUCh. 6.4 - Prob. 80AYUCh. 6.4 - Prob. 81AYUCh. 6.4 - Prob. 82AYUCh. 6.4 - Prob. 83AYUCh. 6.4 - Prob. 84AYUCh. 6.4 - Prob. 85AYUCh. 6.4 - Prob. 86AYUCh. 6.4 - Prob. 87AYUCh. 6.4 - Prob. 88AYUCh. 6.4 - Prob. 89AYUCh. 6.4 - Prob. 90AYUCh. 6.4 - Prob. 91AYUCh. 6.4 - Prob. 92AYUCh. 6.4 - Prob. 93AYUCh. 6.4 - Prob. 94AYUCh. 6.4 - Prob. 95AYUCh. 6.4 - Prob. 96AYUCh. 6.4 - Prob. 97AYUCh. 6.4 - Prob. 98AYUCh. 6.4 - Prob. 99AYUCh. 6.4 - Prob. 100AYUCh. 6.4 - Prob. 101AYUCh. 6.4 - Prob. 102AYUCh. 6.4 - Prob. 103AYUCh. 6.4 - Prob. 104AYUCh. 6.4 - Prob. 105AYUCh. 6.4 - Prob. 106AYUCh. 6.4 - Prob. 107AYUCh. 6.4 - Prob. 108AYUCh. 6.5 - The graph of y= 3x6 x4 has a vertical asymptote....Ch. 6.5 - True or False If x=3 is a vertical asymptote of a...Ch. 6.5 - The graph of y=tanx is symmetric with respect to...Ch. 6.5 - The graph of y=secx is symmetric with respect to...Ch. 6.5 - It is easiest to graph y=secx by first sketching...Ch. 6.5 - True or False The graphs of...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 7-16, if necessary, refer to the...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 17-40, graph each function. Be sure to...Ch. 6.5 - In Problems 41-44, find the average rale of change...Ch. 6.5 - In Problems 41-44, find the average rale of change...Ch. 6.5 - In Problems 41-44, find the average rale of change...Ch. 6.5 - In Problems 41-44, find the average rale of change...Ch. 6.5 - In Problems 45-48, find ( fg )( x )and( gf )( x )...Ch. 6.5 - In Problems 45-48, find ( fg )( x )and( gf )( x )...Ch. 6.5 - In Problems 45-48, find ( fg )( x )and( gf )( x )...Ch. 6.5 - In Problems 45-48, find ( fg )( x )and( gf )( x )...Ch. 6.5 - In Problems 49 and 50, graph each function. f( x...Ch. 6.5 - In Problems 49 and 50, graph each function. g( x...Ch. 6.5 - Carrying a Ladder around a Corner Two hallways,...Ch. 6.5 - A Rotating Beacon Suppose that a fire truck is...Ch. 6.5 - Exploration Graph y=tanxandy=cot( x+ 2 ) Do you...Ch. 6.6 - For the graph of y=Asin( x ) , the number is...Ch. 6.6 - True or False A graphing utility requires only two...Ch. 6.6 - Prob. 3AYUCh. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - Prob. 8AYUCh. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 3-14, find the amplitude, period, and...Ch. 6.6 - In Problems 15-18, write the equation of a sine...Ch. 6.6 - In Problems 15-18, write the equation of a sine...Ch. 6.6 - In Problems 15-18, write the equation of a sine...Ch. 6.6 - In Problems 15-18, write the equation of a sine...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - In Problems 19-26, apply the methods of this and...Ch. 6.6 - Alternating Current (ac) Circuits The current I ,...Ch. 6.6 - Alternating Current (ac) Circuits The current I ,...Ch. 6.6 - Hurricanes Hurricanes are categorized using the...Ch. 6.6 - Monthly Temperature The data below represent the...Ch. 6.6 - Monthly Temperature The given data represent the...Ch. 6.6 - Monthly Temperature The following data represent...Ch. 6.6 - Tides The length of time between consecutive high...Ch. 6.6 - Tides The length of time between consecutive high...Ch. 6.6 - Hours of Daylight According to the Old Farmer’s...Ch. 6.6 - Hours of Daylight According to the Old Farmer's...Ch. 6.6 - Hours of Daylight According to the Old Farmer's...Ch. 6.6 - Hours of Daylight According to the Old Fanner's...Ch. 6.6 - Prob. 39AYUCh. 6.6 - Find an application in your major field that leads...Ch. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - Prob. 4CTCh. 6 - Prob. 5CTCh. 6 - Prob. 6CTCh. 6 - Prob. 7CTCh. 6 - Prob. 8CTCh. 6 - Prob. 9CTCh. 6 - Prob. 10CTCh. 6 - Prob. 11CTCh. 6 - Prob. 12CTCh. 6 - Prob. 13CTCh. 6 - Prob. 14CTCh. 6 - Prob. 15CTCh. 6 - Prob. 16CTCh. 6 - Prob. 17CTCh. 6 - Prob. 18CTCh. 6 - Prob. 19CTCh. 6 - Prob. 20CTCh. 6 - Prob. 21CTCh. 6 - Prob. 22CTCh. 6 - Prob. 23CTCh. 6 - Prob. 24CTCh. 6 - Prob. 25CTCh. 6 - Prob. 26CTCh. 6 - Prob. 27CTCh. 6 - Prob. 28CTCh. 6 - Prob. 29CTCh. 6 - Prob. 1CRCh. 6 - Prob. 2CRCh. 6 - Prob. 3CRCh. 6 - Prob. 4CRCh. 6 - Prob. 5CRCh. 6 - Prob. 6CRCh. 6 - Prob. 7CRCh. 6 - Prob. 8CRCh. 6 - Prob. 9CRCh. 6 - Prob. 10CRCh. 6 - Prob. 11CRCh. 6 - Prob. 12CRCh. 6 - Prob. 13CRCh. 6 - Prob. 14CRCh. 6 - Prob. 15CR
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