Did i do it correct

1. Jan 4, 2004

majinknight

Ok So i finished my questions and was wondering if someone could check my work to see if i did it right.
Question: If CosA= 1/3, with 0<A<pie/2, and SinB=1/4, with pie/2<B<pie, Calculate sin(A+B)

My Solution:

Sin(A+B)= SinACosB + CosASinB
=SinACosB + (1/3)(1/4)
SinACosB + 1/12

Ok Now i drew Triangle A and labeled the bottom 1 and hypotaneous 3. Then used the theorum to get the last side is square root 8.
I made Triangle B and labelled hypotaneous 4, adjacent side being 1 and used theorum to get the opposite side to be square root of 15.

=(square root8/3)(square root15/4) +1/12
=(square root120/12) + 1/12
to get my final answer of squareroot 120 +1 /12.

Is that correct?

2. Jan 4, 2004

HallsofIvy

Staff Emeritus

You are exactly right (and for the right reasons!) that

but then you seem to have lost control of your parentheses.

which is not the same as &radic(120)+ 1/12 which is how I would have interpreted "squareroot 120 +1 /12".

shouldn't cosB be negative for $$\frac{\pi}{2}<B< \pi$$