SOLUTION: What is the exact value of tan(13pi/12)? How do I figure that out? Thank you for your help.

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Question 21469: What is the exact value of tan(13pi/12)? How do I figure that out?
Thank you for your help.
Found 2 solutions by josmiceli, khwang:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%2813%2Api%29+%2F+12+=+%28%2812%2F12%2Api%29+%2B+%281%2F12%2Api%29%29+=+pi+%2B+%28pi%2F12%29
so, the tangent = tan%28pi+%2B+%28pi%2F12%29%29
this puts the angle in the 3rd quadrant where the tangent is positive
the answer is:
tan%28pi%2F12%29

Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
tan(13pi%2F12)
= tan(pi%2F12)
Use cos+2+x+=+2+cos%5E2+x+-1+=+1-+2+sin+%5E2x+
= sin+%28x%2F2%29%2F+cos+%28x%2F2+%29+

We have tan+%28x%2F2%29+=+sqrt+%28%281-cos+x%29%2F%281%2Bcos+x%29+%29
Hence, tan+%28pi%2F12%29+=+sqrt%28%281-cos+%28pi%2F6%29+%29%2F%281%2Bcos+%28pi%2F6%29%29%29
= +sqrt%28%281-+sqrt%283%29%2F2%29%2F%281+%2B+sqrt%283%29%2F2%29%29
= +sqrt%28%281-+sqrt%283%29%2F2%29%5E2%2F+%281%2F2%29%5E2%29+
= 2+-+sqrt%283%29

Kenny