SOLUTION: if sin theta = -5/13 and 3pie/2 < theta < 2pie find the exact values of cos theta if you could show me the steps as well that would be great thank you =)

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Question 323906: if sin theta = -5/13 and 3pie/2 < theta < 2pie
find the exact values of cos theta
if you could show me the steps as well that would be great thank you =)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28theta%29=-5%2F13
You also know that,
%28cos%28theta%29%29%5E2%2B%28sin%28theta%29%29%5E2=1
%28cos%28theta%29%29%5E2%2B%28-5%2F13%29%5E2=1
%28cos%28theta%29%29%5E2%2B25%2F169=1
%28cos%28theta%29%29%5E2=1-25%2F169
%28cos%28theta%29%29%5E2=144%2F169
cos%28theta%29=0+%2B-+12%2F13
Now look at the range you're considering,
(3%2Api%2F2,2pi) or the fourth quadrant.
In that quadrant, the cosine is positive, the sine is negative.
cos%28theta%29=12%2F13