# Finding sine and cosine formulas

1. Oct 31, 2007

### rum2563

[SOLVED] Finding sine and cosine formulas

1. The problem statement, all variables and given/known data
If sinx/siny = 1/2 and cosx/cosy = 3 prove:

sin (x + y) = 7/3 sinx cosx

2. Relevant equations
sin (x + y) = sinx cosy = cosx siny

3. The attempt at a solution

Can someone please give me a hint so that I can start? Thanks.

2. Oct 31, 2007

### rock.freak667

Well fine cosy in terms of cosx from the 2nd formula and find siny in terms of sinx from the 1st formula and sub into the LHS of the proof

3. Oct 31, 2007

### rum2563

Ok, here it goes:

* sinx/siny = 1/2

siny = 2sinx

* cosx/cosy = 3

cosy = cosx/3

sin(x + y) = sinx cosy + cosx siny
= cosx/3 + 3 X 2sinx
= cosx/3 + 6sinx
= 7/3 sinx cosx

Is this possibly right?

4. Oct 31, 2007

### rock.freak667

well that is correct...but you should put in the sinx and cosx in the 2nd and 3rd lines...or else it may seem weird that you simply got back the sinx and cosx at the end

5. Oct 31, 2007

### rum2563

Well, If I put back sinx and cosx, then how will I get rid of them in the end?

6. Oct 31, 2007

### rock.freak667

sin(x + y) = sinx cosy + cosx siny
= (sinxcosx)/3 + 2sinxcosx
=$\frac{7sinxcosx}{3}$

7. Nov 1, 2007

### rum2563

Thanks very much rock.freak667. I finally get this.