SOLUTION: sinx = cos2x Solve the equation?.....is that possible?

Algebra ->  Trigonometry-basics -> SOLUTION: sinx = cos2x Solve the equation?.....is that possible?      Log On


   

Question 341689: sinx = cos2x
Solve the equation?.....is that possible?
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!

Sin%28x%29+=+Cos%282x%29

Use the identity Cos%282theta%29=1-2Sin%5E2theta on the right side:

Sin%28x%29=1-2Sin%5E2x

2Sin%5E2x%2BSin%28x%29-1=0

The left side factors just like 2y%5E2%2By-1 factors as %282y-1%29%28y%2B1%29

%282Sin%28x%29-1%29%28Sin%28x%29%2B1%29=0

Set each factor = 0

Setting the first factor = 0

2Sin%28x%29-1=0
2Sin%28x%29=1
Sin%28x%29=1%2F2
x=%2230%B0%3B150%B0%22

Setting the second factor = 0

Sin%28x%29%2B1=0
Sin%28x%29=-1
x=%22270%B0%22

So there are 3 solutions in degrees between 0° and 360°.

Edwin