SOLUTION: Solve on indicated interval: 0°&#8804;&#920;<2&#960; Find EXACT answers. Sin(2&#920;)Sin(&#920;)=cos(&#920;)

Algebra ->  Trigonometry-basics -> SOLUTION: Solve on indicated interval: 0°&#8804;&#920;<2&#960; Find EXACT answers. Sin(2&#920;)Sin(&#920;)=cos(&#920;)      Log On


   

Question 421985: Solve on indicated interval: 0°≤Θ<2π Find EXACT answers.
Sin(2Θ)Sin(Θ)=cos(Θ)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite sin%282theta%29 as 2sin%28theta%29cos%28theta%29. The equation becomes

2sin%5E2%28theta%29+cos%28theta%29+=+cos%28theta%29

2sin%5E2%28theta%29+cos%28theta%29+-+cos%28theta%29+=+0

cos%28theta%29%282sin%5E2%28theta%29+-+1%29+=+0. Either cos%28theta%29+=+0 or 2sin%5E2%28theta%29+-+1+=+0 --> sin%5E2%28theta%29+=+1%2F2, sin%28theta%29+=+sqrt%282%29%2F2 or sin%28theta%29+=+-sqrt%282%29%2F2.

We evaluate the arcsine or arc-cosine of each to produce all possible values of theta, which are pi%2F2, 3pi%2F2, as well as pi%2F4, 7pi%2F4, 3pi%2F4, 5pi%2F4.