5. Inverse Trigonometric Functions and Basic Trigonometric Equations

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). sin² x - 2 cos x - 2 = 0

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). cos 2x = cos 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. sin 2x = √ 3 sin x

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅). 4 tan² x - 8 tan x + 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.

2√3 sin x/2 = 3

Find all solutions to the equation.

$\(\sqrt\)2\(\cos\]\theta\)+4=5$

In Exercises 97–116, use the most appropriate method to solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 7 cos x = 4 - 2 sin² x

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

sin θ/2 = 0

Find all solutions of each equation. cos x = ﹣1/2

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

Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). sin² θ - 1 = 0

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅). sin x = 0.8246

Find all solutions to the equation.

$\(\cos\) x=1$

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

tan x = cot x