SOLUTION: What is the exact value of tan(cos^-1(-4/7)) ?

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Question 387952: What is the exact value of tan(cos^-1(-4/7)) ?
Found 2 solutions by robertb, user_dude2008:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let alpha+=+cos%5E%28-1%29%28-4%2F7%29. Then cos%28alpha%29+=+-4%2F7, and we have to find the value of tan%28alpha%29. Now cos%28alpha%29+=+-4%2F7---->sec%28alpha%29+=+-7%2F4, so that, by using the identity %28sec%28alpha%29%29%5E2+=+1+%2B+%28tan%28alpha%29%29%5E2, we get 49%2F16+=+1+%2B++%28tan%28alpha%29%29%5E2, or 33%2F16+=+%28tan%28alpha%29%29%5E2.
Then tan%28alpha%29+=+-sqrt%2833%29%2F4. Tangent of alpha is negative because cos%5E%28-1%29%28-4%2F7%29 means alpha is in the 2nd quadrant.

Answer by user_dude2008(1862) About Me  (Show Source):