## Inverse Trigonometric Functions Questions and Answers

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A) Evaluate tan-1(-64) to 2 decimal places in degrees. If necessary, use 3.1416 as an approximation to pi. B) Find the value of cos(sin-1(5/13)) C) Find arccos(-3 \sqrt 2).

What is the maximum value of the function y= 6sin(2x)?

Solve (2\cos\theta + 1)(\sin\theta - 1)= 0 in the interval [0, 2\pi).

What does \arctan 0 equal?

Find the exact value. Give the answer in radians. \tan^{-1}(\frac{-1}{\sqrt{3}})

Find the exact value. Give the answer in radians. \cos^{-1}(\frac{-\sqrt{2}}{2})

Find the exact value of: a. \arccos \left ( \tan \frac{3\pi}{4} \right ) b. \arcsin \left ( \tan \frac{5\pi}{6} \right )

In \triangle ABC, a= 1.3 cm, b= 2.8 cm, \angle A = 33^\circ. Determine the measure of \angle B if it exists.

Evaluate the expression using a calculator and give the answer in degrees. \cos^{-1}(0.5432)

Explain why cos^(-1)(cos 2009) = 2009 is wrong. Why don't the cosine inverse and cosine cancel each other out?

Complete the table. x f(x) f'(x)

Solve the equation 9 \arcsin^2 (x) - \pi^2 = 0

Determine the value of f(x) = 3\sin^{-1}(\sin(x)) + 3\cos^{-1}(\sin(4x)) at x = \frac{\pi}{3} without using a calculator. (Use symbolic notation and fractions where needed.)

If f(x) = \frac{1}{(x - 1)^3} and g(x) = (x - 1)^2, then find the point where \frac{f(x)}{g(x)} is not defined. Also comment on the point where it is being asymptotic.

Explain whether the following statement is true or false. It is impossible to obtain exact values for the inverse secant function.

Suppose y = f(x) and \frac{1}{x} + \frac{1}{y} = 1. Find f^{-1}(x) and verify your answer.

Let a = \arctan(x) and b = \arctan(y) and \tan(a+b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} . Use the identity \tan(a+b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} to show that \arctan(x) + \arctan(y) = \arctan(\frac{x+y}{1 - xy})

Evaluate: \cos (\arcsin(\tan(\arccos (-\frac{\sqrt{2}}{2}))))

The pressure of a fluid flowing through a closed system, P, after t seconds can be modeled by the given function.

What is the domain of the function f (x) = 1 / {square root {9 - x^2}}?

Solve the equation, cos (2 x) = 5 sin(x), giving the exact solutions which lie in [0, 2).

Evaluate the integral based on inverse trigonometric functions. \int \frac{e^{2t}}{e^{4t} + 9} dx

x = 3 \cdot \tan (\theta), f(\theta) = \sin (\theta) \cdot \tan (\theta) (a) Solve for \theta as a function of x. (b) Replace \theta in f(\theta) with your result in part (a), and (c) simplify.

Find all the values of x in the interval [0,2\pi). 2 - 3sin^2x = \cos^4x

Let F(x) = f(f(x)) and G(x) = (F(x))^2. You also know that f(3) = 7, f(7) = 2, f'(7) = 2, f'(3) = 6. Find: F'(3) = \pi and G'(3) = .

Write the following trigonometric expression as an algebraic expression in u: csc (tan^{-1}(u))

Solve. \sin(\cos^{-1} \frac{4}{11})

1. (a)cot^{-1}(-sqrt(3)/3) (b)cot^{-1}(0) 2. (a)cot^{-1}(1) (b)cot^{-1}(-sqrt(3)) 3. (a)sec^{-1}(-2) (b)arccsc(-1) 4. (a)csc^{-1}(2sqrt(3)/3) (b)sec^{-1}(0)

Evaluate the integral. Show all steps. \\ \int \frac{3}{\sqrt{4-x^2}}dx

Find the domain of the function: g(x)=\frac{\sqrt{3-x}}{\ln |x| }

What is the domain of \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}?

Given f(x) = x^3 + x + 3, find (f^{-1})'(5).

Find the exact value of the expression. tan(arctan(1))

Find the derivative: \arctan \sqrt x

How does the domain of the derivative of a trigonometric function compare with the domain of the function?

By using the definition of the inverse function, establish the identity d d x cos - 1 ( x ) = - 1 square root of 1 - x 2

What is the inverse sin of 5x?

Simplify the following expression: 2\cos(\tan^{-1}(\frac{x}{3}))

Write as an algebraic expression not involving any trigonometric functions: \sin(\tan^{-1} u).

Find the exact value arcsin (\frac{\sqrt 2}{2}).

Find the solution, sin^2 \theta + cos \theta = 2.

Find the missing value to the nearest hundredth: tan (blank) = 7.

Find all solutions for the following equation in the interval 0 less than or equal to x less than 2pi 3 cos(3x) = 6

Find the domain of the real valued sine function f given below: f(x) = 2 sin(x - 1)

Suppose f(x) = sin(pi cos(x)). On any interval where the inverse function y = f^-1(x) exists, what is the derivative of f^-1(x) with respect to x ?

Triangle \bigtriangleup ABC is given where \angle A=33^\circ, \text{ and } a = 15 in, and the height, h = 9 in. How many distinct triangles can be made with the given measurements? Explain

Which is the radian measure of an angle whose sine is 0.7? A. 0.64 B. 0.76 C. 0.78 D. 0.80

Domain? \sqrt[3] {\frac{\arccos(x^2 - 2)}{\cos x}}

Evaluate the integral. \int_{0}^{3} \sqrt{x^2 + 9} dx

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A, B, C, D, or E) in each blank. A. \tan(\arcsin

Use a calculator to find the value of \sec 3.125

I f(x) 5e^{4-x} - 11e^{3x-12} - 4x a) analytically show f is 1 to -1 b) find (f^{-1})(-22)

Find the exact value of each expression. 1) Sin^{-1}(fraction {-1}{2}) 2) cos^{-1} ( fraction {square root 2}{2}) 3) cos^{-1}( fraction {-square root 3}{2}) 4) tan^{-1} (square root 3)

Determine (at least approximately) the interval in which the solution is defined. (Round your answer to two decimal places.) y = 1 / 3 (pi - arcsin (3 cos^2 (x))).

Sketch the graph of y = \cos^{-1} \left(\cos(x) \right) .

Using inverse trigonometric functions, find a solution to the equation cos(x)=0.2 in the interval [0, 4] Then, use a graph to find all other solutions to this equation in this interval.

An auditorium with a flat floor has a large screen on one wall. The lower edge of the screen is 3 feet above eye level and the upper edge is 10 feet above eye level. Assume you walk away from the scre

Find: can you show that \tan{-1} x+\tan{-1}y=C_1 , is equal to \frac{(x+y)}{(1-xy)}=C_1 and C_1 is a constant.

Differentiate fx=arccos(x) Show triangle

Use \theta= \arctan \frac{28}{x} - \arctan \frac{6}{x} to show that \theta also equals \arctan \frac{22x}{x^2 +168}.