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.
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{{{sin(pi/10) = (sqrt(5) - 1)/4}}}
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For pi/5 use:
sin(2x) = 2sin(x)*cos(x)
{{{cos(x) = sqrt(1 - sin^2(x))}}}
As a check, {{{sin(pi/5) = sqrt(10 - 2sqrt(5))/4}}}
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For pi/20, use a half-angle formula.
The simplest is:
{{{sin^2(A/2) = (1 - cos(A))/2}}}
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To check:  {{{sin(pi/20) = (sqrt(8 -2(sqrt(10 + 2sqrt(5)))))/4}}}
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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.