# Trig. Identity

1. Oct 29, 2009

### morr485

1. Verify this identity: a*sin Bx + b*cos Bx = sqrt(a^2 + b^2)sin(Bx + C)
where C= arctan b/a

2. a/sqrt(a^2+b^2)sin Bx + b/sqrt(a^2+b^2)cos Bx=cos C sin Bx + sin C cos Bx=

3.a*sin Bx + b cos Bx = sqrt(a^2 + b^2) sin(Bx + C)

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Oct 30, 2009
2. Oct 30, 2009

### danago

First thing that jumps to my mind is to make use of the trig expansion:

$$R sin(Bx+C)=R(sin(Bx) cos(C)+cos (Bx)sin(C))$$

3. Oct 30, 2009

### morr485

danago thanks for the hint.