SOLUTION: Use a compound angle formula to demonstrate that sin(2π-x) = -sin(x).

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Question 1205299: Use a compound angle formula to demonstrate that sin(2π-x) = -sin(x).
Answer by ikleyn(52898) About Me  (Show Source):
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Use a compound angle formula to demonstrate that sin(2π-x) = -sin(x).
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Use the general formula for the sine function with the difference of arguments 


    sin(a-b) = sin(a)*cos(b) - cos(a)*sin(b).



Take a = 2pi, b = x.  You will get


    sin%282pi-x%29 = sin%282pi%29%2Acos%28x%29 - cos%282pi%29%2Asin%28x%29 = 0*cos(x) - 1*sin(x) = 0 - sin(x) = -sin(x).

QED

Solved.