Question

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)

Answer 1

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.

Answer 2

i got 15/17

Answer 3

\[\sin A = \frac{3}{5} \implies \cos A = \frac{4}{5} \text{ (in the given interval)} \]
\[\cos B = \frac{12}{13} \implies \sin B = \frac{5}{13} \text{ (in the given interval)} \]

\[\cos A + B = \cos A \cos B - \sin A \sin B = \frac{4}{5}\cdot \frac{12}{13} - \frac{3}{5}\cdot \frac{5}{13} = \frac{33}{65}\]

Answer 4

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