5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

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

θ = csc⁻¹ (-2)

Solve each equation for exact solutions.

cos⁻¹ x + tan⁻¹ x = π/2

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

θ = sin⁻¹ 2

Use a calculator to approximate each value in decimal degrees.

θ = sin⁻¹ (-0.13349122)

Solve each equation for exact solutions.

tan⁻¹ x - tan⁻¹ (1/x ) = π/6

Which one of the following equations has solution π?

a. arccos (―1) = x

b. arccos 1 = x

c. arcsin (―1) = x