5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

y = 6 cos x/4 , for x in [0, 4π]

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

Write each trigonometric expression as an algebraic expression in u, for u > 0.

sin (arccos u)

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

y = cos⁻¹ (―1)

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. cos⁻¹ 3/8

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

θ = csc⁻¹ (-2)

Solve each equation for x.

arccos x + arctan 1 = 11π/12

Use a calculator to approximate each value in decimal degrees.

θ = tan⁻¹ (-7.7828641)

Evaluate each expression without using a calculator.

tan (arccos 3/4)

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

Evaluate each expression without using a calculator.

sin (2 tan⁻¹ (12/5))

Use a calculator to find each value. Give answers as real numbers.

tan (arcsin 0.12251014)

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

In Exercises 1–26, find the exact value of each expression. _ sec⁻¹ (−√2)

Evaluate the expression.

$\(\cos\)^{-1}\(\left\)(-1\(\right\))$