Expert: Paul Klarreich - 5/15/2007

Question
Hi Mr.! I need some help on this..I have no idea how to do this..

3. Derive a formula for sin3x that will only have sin x and powers of sin x terms.

thanks in advance!

Answer
Questioner:   Kay
Category:  Advanced Math
 
Subject:  pre-calc
Question:  Hi Mr.! I need some help on this..I have no idea how to do this..

3. Derive a formula for sin3x that will only have sin x and powers of sin x terms.

>> 3.?? What happened to 1. and 2.?

thanks in advance!
........................................
Hi, Kay,

Don't be put off by the title.  Some day....

sin(3x) = sin(2x + x) =

sin 2x cos x + cos 2x sin x

2 sin x cos x cos x + (1 - 2 sin^2 x) sin x

2 sin x cos^2 x + (1 - 2 sin^2 x) sin x

2 sin x (1 - sin^2 x) + (1 - 2 sin^2 x) sin x

Now multiply out and expand:[ S stands for sin x ]

2 S (1 - S^2) + (1 - 2 S^2) S

2S - 2S^3 + S - 2S^3

3S - 4S^3