## anonymous 5 years ago If A and B are positive acute angles, sin A=3/5, and cos B=12/13, what is the exact value of cos (A+B)

1. anonymous

sinA=3/5 arcsin(3/5)=A A=36.8699 cosB=12/13 arccos(12/13)=B B=22.6199 cos(36.8699+22.6199) is approximately .50769.

2. anonymous

i got 15/17

3. anonymous

$\sin A = \frac{3}{5} \implies \cos A = \frac{4}{5} \text{ (in the given interval)}$ $\cos B = \frac{12}{13} \implies \sin B = \frac{5}{13} \text{ (in the given interval)}$ $\cos A + B = \cos A \cos B - \sin A \sin B = \frac{4}{5}\cdot \frac{12}{13} - \frac{3}{5}\cdot \frac{5}{13} = \frac{33}{65}$

4. anonymous

If A is in quadrant II and cos A=-3/4, find an exact value for sin 2A