5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

Given the function $y=cot\left(x\right)$, which of the following statements is true about its inverse function $y=arccot\left(x\right)$?

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(cot⁻¹ 9π)

Evaluate each expression without using a calculator.

sin (arccos (3/4))

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ csc(tan⁻¹ √3/3)

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ 0.3

Evaluate the expression.

$\(\sin\)^{-1}\(\left\)(\(\frac{\sqrt2}{2}\]\right\))$

Use a calculator to approximate each value in decimal degrees.

θ = cos⁻¹ 0.80396577

Use a calculator to approximate each value in decimal degrees.

θ = arctan 1.7804675

Find the exact value of each real number y. Do not use a calculator.

y = arccot (―1)

Evaluate the expression.

$\(\cos\)^{-1}\(\left\)(-\(\frac{\sqrt2}{2}\]\right\))$

Find the degree measure of θ if it exists. Do not use a calculator.

θ = cot⁻¹ (-√3/3)

In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ (−√3)

Find the exact value of each real number y if it exists. Do not use a calculator.

y = tan⁻¹ 1

Evaluate each expression without using a calculator.

tan⁻¹ (tan (π/4))