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). 9 tan² x - 3 = 0

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

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

cos θ/2 = -1/2

Use substitution to determine whether the given x-value is a solution of the equation.

$\tan 2x=-\frac{\sqrt{3}}{3},x=\frac{5\pi }{12}$

Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). 2 sin² x = sin x + 3

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

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

Solve each equation for all exact solutions, in degrees.

2√3 cos (θ/2) = -3

Exercises 25–38 involve equations with multiple angles. Solve each equation on the interval [0, 2𝝅).

cot(3θ/2) = ﹣√3

Find all solutions of each equation. sin x = (√3)/2

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

sin θ/2 = -√3/2

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

(cot θ ―√3) (2 sin θ + √3) = 0

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

cos² x + 2 cos x + 1 = 0

In Exercises 121–126, solve each equation on the interval [0, 2𝝅). 3 cos² x - sin x = cos² x

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