Question

if csc theta = -5/3 and theta has its terminal side in quadrant III, find the exact value of tan 2 theta.

Answer 1

I would do a doodle of a right triangle in quadrant 3 with csc(theta)=-5/3

Answer 2

label the sides with the correct measurement

Answer 3

\[\tan(2 \theta)=\frac{\sin(2 \theta)}{\cos( 2 \theta)}=\frac{ 2 \sin(\theta) \cos(\theta)}{\cos^2(\theta)-\sin^2(\theta)}\]

Answer 4

then you can find tan(2 theta) by using your triangle