Note that cos theta = adj / hyp, and that we can therefore assume that adj = -8 and hyp = 17. With theta in Q III, the opp side must be negative. What is it? Use the Pyth. Thm. to find the opp side:
17^2 = (-8)^2 + opp^2 => 289 = 64 + |opp|^2. Then, in Q III, opp = sqrt(225) = -15.
In summary, opp = -15, adj = -8 and hyp = 17.
cos 2 theta = cos theta cos theta - sin theta sin theta, or
(cos theta)^2 - (sin theta)^2
= (-8/17)^2 - (-15/17)^2 = approx 0.221 - 0.779 = -0.558 (ans)
Review: cos 2 theta = (cos theta)^2 - (sin theta)^2
sin 2 theta = 2(sin theta)(cos theta)
2 tan theta
tan 2 theta = -----------------------
1 - (tan theta)^2
