In Problems 77-88, use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator. 77. sin 40° + cos? 40° 78. sec? 18° – tan 18° \ 79. sin 80° csc 80° 80. tan 10° cot 10° sin 40° cos 20° 81. tan 40° 82. cot 20° 83. cos 400° - sec 40° 84. tan 200° - cot 20° cos 40° sin 20° 85. sin(-) se 2 37 COs 18 sin (- 20°) 87. sin 70° csc 86. sec + tan 200° 88. + tan(-70°) 18 cos 380° cos (-430°)

Q: If e = 26, then x =

A: Given  e7x=26 We have to find the value of x.

Q: Find the largest value of x that satisfies: loge (2) – log,(r + 1) = 6

A: Use the properties of logarithmic function, to rewrite the given equation.…

Q: 9. In what situation would you use the sine or cosine laws rather than just simple trigonometric…

A:

Q: point(s)  (6.1,y) is/are on the circle  x2+y2=49. Determine the missing coordinate(s) and enter the…

A:

Q: 6. The point A (6, -2) is on the terminal side of an angle in standard position. Determine the exact…

A: The figure

Q: (a) 1² + 4.x + 3

A: Here we have to evaluate the integration by using trigonometric substitution method.

Q: What is the photon frequency (Terahertz = 1012 Hz) needed to move an electron in 1 to a higher…

A: We will find out the required value.

Q: 7. Use Trigonometric Substitution to evaluate -1

A: Here we have to integrate by the trigonometric substitution.  I=∫x3x2-1dx

Q: Find x, if artan x/2 = pi/4

A: arc tan (x/2 )= pi/4 and as we know tan(pi/4) = 1

Q: . tan-1 (- 1) =_____________

A: Given expression: tan-1-1 Consider the value of tan-1-1=x Then, tanx=-1

Q: 4. Use Regiomontanus' sine table to find the remaining angles in the right triangle if you know that…

A: Answers are following in explanation step.Explanation:

Q: 3. (7x – 1)- 125°

A:

Q: Tan ( 3θ - 4 degrees ) = 1/ cot ( 5θ - 8 degrees)

A: Solve:

Q: In Problems 35–46, convert each angle in degrees to radians. Express your answer as a multiple of T.…

A:

Q: 4. 2 -2 -4- -6+ -8-

A: The objective is to find period and amplitude of the given function.

Q: Find the exact value: (no calculators!) V3 -1 tan 3

A: to find:- exact value.

Q: Evaluate the expression arcsec 2 without using a calculator.

A: Given,         arcsec 2

Q: La Grande Roue de Montréal is the largest Ferris wheel in Canada and the fourth largest in the…

A:

Q: Example 2.22. Use the method of false position, to find the fourth root of 32 correct to three…

A:

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.