Use a calculator to solve the equation on the interval [0, 2π). Round to the nearest hundredth of a radian. sin 2x - sin x = 0 : 0, 1.05, 3.14, 5.24 1.05, 3.14, 5.24 0, 2.09, 4.19 0, 2.09, 3.14, 4.19

Sin 2x - sin x=0

Using the trigonometric identity: sin 2x=2 sinx cosx

2 sinx cosx - sinx = 0

Common factor sinx

sinx (2 cosx - 1) = 0

Two options:

1) sinx=0

on the interval [0,2π), the sinx=0 for x=0 and x = π=3.1416→x=3.14

2) 2 cosx - 1=0

Solving for cosx

2 cosx-1+1=0+1

2 cosx = 1

Dividing by 2 both sides of the equation:

(2 cosx) / 2=1/2

cosx=1/2

cosx is positive in first and fourth quadrant:

First quadrant cosx=1/2→x=cos^ (-1) (1/2) →x = π/3=3.1416/3→x=1.05

Fourth quadrant: x = 2π-π/3 = (6π-π) / 3→x=5 π/3=5 (3.1416) / 3→x=5.24

Answer: Solutions: x=0, 1.05, 3.14, and 5.24