1. ## Sin Cos Tan...

I thought I knew how to work out these equations, but my answer was different from the answer they gave.

Given: a and B are first-quadrant angles, sin a = 5/13 and cos B = 3/5, evaluate cos (a+B).

I used the equations sin^2 a + cos^2 a = 1 to get cos a = 12/13. That would make cos (a+B) 99/65. However, their answer was 16/65. Help, please? Another one:

Given: a and B are first-quadrant angles, sin a = 5/13 and cos B = 3/5, evaluate sin (a-B).

I used the same equations to get sin B = 4/5, and thus sin (a-B) = -27/65. Their answer was -33/65. Please help me out!!!

~Cassie

2. You got wrong answers because you thought
cos(a+B) = cos(a) +cosB, and sin(a-B) = sin(a) -sinB.

No.
The correct expansions are:
cos(a+B) = cos(a)*cosB -sin(a)*sinB.
And, sin(a-B) = sin(a)*cosB -cos(a)*sinB

So, get all the sines and cosines of angles "a" and B, then solve your questions again. You will get them this time.

3. Ah, I reworked them and got it! Thanks so much!!!!