SOLUTION: Given that the exact value of sin pi/10 = -1+√5 divided by 4, for each question calculate the exact value of the expression. You may leave nested radicals in your answer, but

Algebra ->  Trigonometry-basics -> SOLUTION: Given that the exact value of sin pi/10 = -1+√5 divided by 4, for each question calculate the exact value of the expression. You may leave nested radicals in your answer, but      Log On


   

Question 1125859: Given that the exact value of sin pi/10 = -1+√5 divided by 4, for each question calculate the exact value of the expression. You may leave nested radicals in your answer, but rationalize any denominaters.
sin pi/5
sin pi/20
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given that the exact value of sin pi/10 = -1+√5 divided by 4, for each question calculate the exact value of the expression.
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sin%28pi%2F10%29+=+%28sqrt%285%29+-+1%29%2F4
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For pi/5 use:
sin(2x) = 2sin(x)*cos(x)
cos%28x%29+=+sqrt%281+-+sin%5E2%28x%29%29
As a check, sin%28pi%2F5%29+=+sqrt%2810+-+2sqrt%285%29%29%2F4
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For pi/20, use a half-angle formula.
The simplest is:
sin%5E2%28A%2F2%29+=+%281+-+cos%28A%29%29%2F2
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To check: sin%28pi%2F20%29+=+%28sqrt%288+-2%28sqrt%2810+%2B+2sqrt%285%29%29%29%29%29%2F4
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These can be tedious and error-prone.
There's no purpose in someone doing them for you.
Not much purpose in you doing them.