SOLUTION: Find the exact value of csc(pi/8)

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Question 749962: Find the exact value of csc(pi/8)
Found 2 solutions by lwsshak3, Alan3354:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of csc(pi/8)
csc(pi/8)=1/sin(pi/8)
half-angle formula for sin: sin%28x%2F2%29=sqrt%28%281-cos%28x%29%29%2F2%29

csc(pi/8)=1/sin(pi/8)=2%2Fsqrt%282-sqrt%282%29%29
..
Check with calculator (use sin function)
sin(pi/8)≈0.3827..
exact value=sqrt%282-sqrt%282%29%29%2F2≈0.3827..

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!

csc(pi/8)=1/sin(pi/8)=2%2Fsqrt%282-sqrt%282%29%29
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csc^2 = 4%2F%282+-+sqrt%282%29%29
= 4%282+%2B+sqrt%282%29%29%2F2
= 2%282+%2B+sqrt%282%29%29
= 4+%2B+sqrt%288%29
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csc%28pi%2F8%29+=+sqrt%284+%2B+sqrt%288%29%29