Sin 2 theta - sin theta = 0

Question

where 0 is less than equal to theta less than equal to 2 pi?  

 

 

Answer 1

Sin 2 theta - sin theta = 0

2Sin theta cos theta - sin theta = 0

Sin theta (2cos theta- 1) = 0

Sin theta=0   

General solution theta =npi±(-1)^n(0) = npi

n=0     theta =0

n=1     theta =pi

n=2     theta =2pi

2cos theta- 1=0                   

cos theta= 1/2

 cos theta =cos pi/3

General solution theta =2npi±pi/3

n=0     theta =pi/3

n=1     theta =5pi/3