5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

y = sec⁻¹ 1

Evaluate each expression without using a calculator.

tan (arcsin (3/5) + arccos (5/7))

Solve each equation for exact solutions.

arcsin x = arctan 3/4

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

y = csc⁻¹ √2/2

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

tan (arcsec (√1―u²) / u)

Solve each equation for exact solutions.

2 arccos (x/3 - π/3) = 2π

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

θ = arctan (-1)

Solve each equation for exact solutions.

sin⁻¹ x - tan⁻¹ 1 = -π/4

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

θ = arcsin (-√3/2)

The point (π/4, 1) lies on the graph of y = tan x. Therefore, the point _______ lies on the graph of y = tan⁻¹ x.

Solve each equation for exact solutions.

arccos x + 2 arcsin √3/2 = π

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

θ = arccos (-1/2)

Solve each equation for exact solutions.

sin⁻¹ x - 4 tan⁻¹ (-1) = 2π

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

θ = cot⁻¹ (-√3/3)

Solve each equation for exact solutions.

arcsin 2x + arccos x = π/6