5. Inverse Trigonometric Functions and Basic Trigonometric Equations

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan⁻¹ (tan 2π/3)

For which interval of $x$ is the cancellation property ${\sin }^{-1}\left(\sin \right(x\left)\right)=x$ valid?

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

y = sec⁻¹ (―1.2871684)

Evaluate each expression without using a calculator.

cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))

Solve each equation for exact solutions.

cos⁻¹ x = sin⁻¹ 3/5

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

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

Find the exact value of each expression. sin⁻¹ 1/2

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

y = cos⁻¹ (―0.32647891)

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

y = sin⁻¹ √3

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

y = sin⁻¹ 0

Use a calculator to approximate each value in decimal degrees.

θ = arcsec 3.4723155

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

y = cos⁻¹ (―√2/2)

Solve each equation for exact solutions.

4/3 cos⁻¹ x/4 = π