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. tan x = 2 cos x tan x

Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). 4 cos² x - 1 = 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

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

2sin x + 3 = 4

In Exercises 53–62, solve each equation on the interval [0, 2𝝅). cot x (tan x - 1) = 0

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

cos 2x = 1/2

Find all solutions to the equation.

$\(\sqrt\)3\(\tan\]\theta\)-7=-6$

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. cos x - 5 = 3 cos x + 6

In Exercises 53–62, solve each equation on the interval [0, 2𝝅). sin x + 2 sin x cos x = 0

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?

Find all solutions of each equation. 2 cos x + √ 3 = 0

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

cos 2x = -1

Use the unit circle shown here to solve each simple trigonometric equation. If the variable is x, then solve over [0, 2π). If the variable is θ, then solve over [0°, 360°).                     

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cos θ = ―1/2

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. 3 tan² x - tan x - 2 = 0

Answer each question.

Suppose solving a trigonometric equation for solutions over the interval [0°,360°) leads to 3θ = 180°, 630°, 720°,930°. What are the corresponding values of θ?