Compound angles question Rsin...

Hello

I have a compound angles question that I have attempted but I am not sure if it is correct or not.

The question and my educated answer is laid out below:

**Express 3sin(A) + 2cos(A) in the form, Rsin(A+****α) **

Now I have done the following after looking through books and teaching myself so it may not be right!

**3sin(A) + 2cos(A) =****Rsin(A+****α)**

= **R(sinA cosα + cosA sinα)**

= (Rcos**α) sinA + (Rsin****α) cosA**

Equating coefficients of sinA gives:

3 = Rcos**α , from which cos****α = 3/R**

**Equating coefficients of cosA gives:**

2= Rsin**α , from which sin****α = 2/R**

R= (square root of) (3squared + 2 squared)

= **(square root of) 13**

= 3.6

So so sorry about the confusion with the symbols and what not...

can anyone tell me if its right or if its not can they guide me in the right direction, sorry about the long winded post (Headbang)

Rob