SOLUTION: given sin(theta)= -1/5 and tan(theta)< 0, find the exact value of cos(theta)

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Question 378975: given sin(theta)= -1/5 and tan(theta)< 0, find the exact value of cos(theta)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If sin(theta) = -1/5 then by the Pythagorean identity,
%28-1%2F5%29%5E2%29+%2B+cos%5E2%28theta%29+=+1
cos%5E2+%28theta%29+=+24%2F25
cos%28theta%29+=+%282%2Asqrt%286%29%29%2F5 (plus or minus)
However, since tan(theta) < 0 and sin(theta) < 0, it follows that cos (theta) > 0 because sin%28theta%29%2Fcos%28theta%29+=+tan%28theta%29 by definition. Therefore we take the positive value of cos(theta), or %282sqrt%286%29%29%2F5.