SOLUTION: If sec(theta)=4, and sin(theta)< 0, find the exact value of cot(theta)?

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Question 593635: If sec(theta)=4, and sin(theta)< 0, find the exact value of cot(theta)?
Answer by danarusu(2) About Me  (Show Source):
You can put this solution on YOUR website!
What we know:
cos(theta)*sec(theta) = 1          (I)
cot%28theta%29+=+cos%28theta%29%2Fsin%28theta%29                        (II)
cos%5E2%28theta%29+%2B+sin%5E2%28theta%29+=+1+                (III)
sec(theta) = 4                        (IV)
sin(theta) < 0                        (V)


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From (I)+(IV) => cos%28theta%29+=+1%2F4                                   (I*)
From (I*)+(III) => sin%28theta%29+=+-sqrt%2815%29%2F4 or sin%28theta%29+=+sqrt%2815%29%2F4 (II*)
From (II*)+(V) =>sin%28theta%29+=+-sqrt%2815%29%2F4                           (III*)
From (II)+(III*) => cot%28theta%29+=+%281%2F4%29%2A%28-4%2Fsqrt%2815%29%29+=+-sqrt%2815%29%2F15+=+-0.258


Final answer: cot(theta) = -0.258