math
posted by Melanie .
suppose that sin0=5/13 and that 0 is a quadrant III angle. what is the exact value of cos0

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 rightangled triangle in quad III, with hypotenuse 13 and opposite 5.
By Pythagoras the adjacent would be 12 (the 51213 triangle)
so cosØ = 12/13 ( by CAST, in III the cosine is negative)
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