5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Use a calculator to approximate each value in decimal degrees.

θ = sin⁻¹ (-0.13349122)

In Exercises 55–62, use the properties of inverse functions f(f⁻¹ (x)) = x for all x in the domain of f⁻¹ and f⁻¹(f(x)) for all x in the domain of f, as well as the definitions of the inverse cotangent, cosecant, and secant functions, to find the exact value of each expression, if possible. cot⁻¹ (cot 3π/4)

The point (π/4, 1) lies on the graph of y = tan x. Therefore, the point _______ lies on the graph of y = tan⁻¹ x.

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin⁻¹(cos 2π/3)

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)

y = arcsin 0.92837781

Solve each equation for x.

y = 1/2 tan (3x + 2), for x in [-2/3 - π/6, -2/3 + π/6]

Evaluate the expression.

$\(\sin\)^{-1}1$

Solve each equation for x, where x is restricted to the given interval.

y = sin x ―2 , for x in [―π/2. π/2]

Decide whether each statement is true or false. If false, explain why.

The tangent and secant functions are undefined for the same values.

Solve each equation for exact solutions.

cos⁻¹ x + tan⁻¹ x = π/2

Evaluate each expression without using a calculator.

arccos (cos (3π/4))

Evaluate the expression.

$\(\tan\)^{-1}\(\left\)(-\(\frac{\sqrt3}{3}\]\right\))$

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin⁻¹ (sin 5π/6)

Solve each equation for x, where x is restricted to the given interval.

y = ―4 + 2 sin x , for x in [―π/2. π/2]

Solve each equation for exact solutions.

arccos x + 2 arcsin √3/2 = π