Answer
a. $-\frac{4}{5}$
b. $\frac{5}{13}$
c. $\frac{33}{65}$
d. $-\frac{56}{65}$
Work Step by Step
a. Knowing $\alpha$ is in quadrant II, we have
$cos\alpha\lt0$ and $cos\alpha=-\sqrt {1-sin^2\alpha}=-\frac{4}{5}$
b. Knowing $\beta$ is in quadrant II, we have
$sin\beta\gt0$ and $sin\beta=-\sqrt {1-cos^2\beta}=\frac{5}{13}$
c. Using the addition formula, we have
$cos(\alpha+\beta)=(-\frac{4}{5})(-\frac{12}{13})-(\frac{3}{5})(\frac{5}{13})=\frac{33}{65}$
d. Using the addition formula, we have
$sin(\alpha+\beta)=(\frac{3}{5})(-\frac{12}{13})+(-\frac{4}{5})(\frac{5}{13})=-\frac{56}{65}$
