NAME

5-3

DATE

PERIOD

Practice Solving Trigonometric Equations

Solve each equation for all values of x. 1. cos x = 3 cos x - 2

3.

√ cos x

= 2 cos x - 1

2. 2 sin2 x - 1 = 0

4. 2 sin2 x - 5 sin x + 2 = 0

Find all solutions of each equation on the interval [0, 2π). 5. sec2 x + tan x = 1

6. 3 tan x - √ 3=0

7. 4 sin2 x - 4 sin x + 1 = 0

8. 4 cos2 x - 1 = 0

3 x − 9. cos = cot x

sin x

10. tan x sin2 x = 3 tan x

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

11. CIRCLES To find the diameter d of any circle, first inscribe a triangle in the circle. The diameter is then equal to the ratio of any side of the triangle and the sine of its opposite angle. a. Suppose the measure of one side of a triangle inscribed in a circle is 20 centimeters. If the measure of the angle in the triangle opposite this side is 30°, what is the length of the diameter of the circle?

b. Suppose a circle with a diameter of 12.4 inches circumscribes a triangle with one side of the triangle measuring 4.6 inches. What is the measure of the angle in the triangle opposite this side? 12. AVIATION An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. Given the formula H = d tan θ, where H is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent θ at which the plane took off.

Chapter 5

18

Glencoe Precalculus