5. Inverse Trigonometric Functions and Basic Trigonometric Equations

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. sin 2x = √ 3 sin x

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 5 cos² x - 3 = 0

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 2 sin² x + sin x - 2 = 0

Solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. sin 2x + cos x = 0

In Exercises 12–18, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 2 sin² x + cos x = 1

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

3 csc x― 2√3 = 0

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

cos θ + 1 = 0

Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate.

2 tan x -1 = 0

Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate.

tan x = cot x

Solve for exact solutions over the interval [0, 2π).

cos 2x = 1/2

Solve for exact solutions over the interval [0, 2π).

cos 2x = -1

Solve for exact solutions over the interval [0°, 360°).

sin θ/2 = 0

Solve for exact solutions over the interval [0°, 360°).

cos θ/2 = -1/2

Solve for exact solutions over the interval [0°, 360°).

sin θ/2 = -√3/2

Answer each question.

Suppose solving a trigonometric equation for solutions over the interval [0, 2π) leads to 2x = 2π/3, 2π, 8π/3. What are the corresponding values of x?