5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Evaluate each expression without using a calculator.

tan⁻¹ (tan (π/4))

Solve each equation for exact solutions.

6 sin⁻¹ x = 5π

Solve each equation for exact solutions.

2 arccos (x/3 - π/3) = 2π

Give the degree measure of θ. Do not use a calculator.

θ = arcsin (―√3/2)

Solve each equation for exact solutions.

tan⁻¹ x = cot⁻¹ 7/5

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

θ = arctan (-1)

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

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

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

y = sec⁻¹ (―2)

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

y = arccos (―√3/2)

Evaluate each expression without using a calculator.

sin (sin⁻¹ 1/2 + tan⁻¹ (-3))

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin(cos⁻¹ 3/5)

Use a calculator to approximate each value in decimal degrees.

θ = csc⁻¹ 1.9422833

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

cos (tan⁻¹ 0.5)