Posted by Melanie on Sunday, July 29, 2012 at 9:09pm.
The "reference angle" that theta makes with the -x axis is sin^-1(5/13) . The cosine of that angle is 12/13.
(Think of a 5:12:13 right triangle)
Cosine is negative in the third quadrant.
The answer is -12/13
make a sketch of the right-angled triangle in quad III, with hypotenuse 13 and opposite 5.
By Pythagoras the adjacent would be 12 (the 5-12-13 triangle)
so cosŲ = -12/13 ( by CAST, in III the cosine is negative)
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