CPM Homework Help : PC3 Problem 8-122

Angles $u$ and $v$ are in the same quadrant. If $\cos(u)=\frac{8}{17}$ and $\sin(v)=-\frac{9}{41}$ , evaluate:

Hint:

If cosine is positive and sine is negative, which quadrant are $u$ and $v$ in?

More Help:

Draw a triangle diagram for each angle. One is done for you.

Right triangle, horizontal leg, labeled 8, on top, vertical leg labeled, square root of quantity 17 squared minus 8 squared, = 15, on right, hypotenuse labeled 17, angle opposite vertical leg, labeled, u.

$\tan\left(u + v\right)$
Hint (a):
$\frac{\tan(u)+\tan(v)}{1-\tan(u)\tan(v)}$
Step (a):
$\frac{\left(\frac{-15}{8}\right)+\tan(v)}{1-\left(\frac{-15}{8}\right)\tan(v)}$

$\cos\left(v-u\right)$
Hint (b):
$\cos(v)\cos(u)+\sin(v)\sin(u)$
Step (b):
$\cos(v)\left(\frac{8}{17}\right)+\sin(v)\left(\frac{-15}{17}\right)$