5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Solve each equation for x.

4/3 arctan x/2 = π

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

cos (arcsin u)

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

sin (2 sec⁻¹ u/2)

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)

Which one of the following equations has solution π?

a. arccos (―1) = x

b. arccos 1 = x

c. arcsin (―1) = x

Evaluate each expression without using a calculator.

cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))

In Exercises 63–82, use a sketch to find the exact value of each expression. cos [tan⁻¹ (− 2/3)]

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)

In Exercises 63–82, use a sketch to find the exact value of each expression. cos (sin⁻¹ 4/5)

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