5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅). cos x = ﹣ 2/5

Find all solutions to the equation.

$3\(\sin\]\theta\)-6=-9$

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

Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). sec² x - 2 = 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 - sin 2θ = 4 sin 2θ

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. 2 cos 2x + 1 = 0

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). sin ( x + 𝝅/4) + sin ( x - 𝝅/4 ) = 1

Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.

3 tan 3x = √3

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

tan θ ―cot θ = 0

Exercises 25–38 involve equations with multiple angles. Solve each equation on the interval [0, 2𝝅). tan(x/2) = √3

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅). tan x = ﹣3

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. cos 2x = -1

Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.

sin 3θ = -1