SOLUTION: Evaluate the expression without using a calculator. cos(sin^-1(1/2))

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Question 1203814: Evaluate the expression without using a calculator.
cos(sin^-1(1/2))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate the expression without using a calculator.
+cos%28sin%5E-1%281%2F2%29%29

let +sin%5E-1%281%2F2%29=x

then +sin%28x%29=1%2F2


then use identity +cos%28x%29=sqrt%281-sin%5E2%28x%29%29 and substitute sin
+cos%28x%29=sqrt%281-%281%2F2%29%5E2%29

+cos%28x%29=sqrt%281-1%2F4%29

+cos%28x%29=sqrt%283%2F4%29

+cos%28x%29=sqrt%283%29%2Fsqrt%284%29

+cos%28x%29=sqrt%283%29%2F2