SOLUTION: Write the expression equivalent to cos 3 theta

Algebra ->  Trigonometry-basics -> SOLUTION: Write the expression equivalent to cos 3 theta      Log On


   

Question 757630: Write the expression equivalent to cos 3 theta
Found 3 solutions by Alan3354, MathLover1, pmatei:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write the expression equivalent to cos 3 theta
------------
cos(3theta) = 4cos^3(theta) - 3cos(theta)

Answer by MathLover1(20855) About Me  (Show Source):
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!

cos%282%2Atheta%29+=+%28cos%28theta%29%29%5E2-%28sin%28theta%29%29%5E2
sin%282%2Atheta%29+=+2+sin%28theta%29+cos%28theta%29
Replacing lines 2 and 3 into the first one and a bit of algebra:
cos%283%2Atheta%29+=+%28cos%28theta%29%29%5E3-3+cos%28theta%29+%28sin%28theta%29%29%5E2
If you want only cosine functions replace %28sin%28theta%29%29%5E2+=+1-%28cos%28theta%29%29%5E2:
cos%283%2Atheta%29+=+4+%28cos%28theta%29%29%5E3+-+3+cos%28theta%29