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=5π/3=5(3.1416)/3→x=5.24

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