SOLUTION: write the expression in terms of sine only 3sin(piX)+3sqrt3cos(piX)

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Question 979237: write the expression in terms of sine only
3sin(piX)+3sqrt3cos(piX)
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!

3%2Asin%28pi%2AX%29 + 3%2Asqrt3%2Acos%28pi%2AX%29 = 3%2A2.%28%281%2F2%29%2Asin%28pi%2AX%29+%2B+%28sqrt%283%29%2F2%29%2Acos%28pi%2AX%29%29 = 6.%28sin%28pi%2F6%29%2Asin%28pi%2AX%29+%2B+cos%28pi%2F6%29%2Acos%28pi%2AX%29%29 = 6.sin%28pi%2F6+%2B+pi%2AX%29 = 6.sin%28pi%2A%281%2F6+%2B+X%29%29.

We used here the addition formula for sines

sin%28alpha+%2B+beta%29 = sin%28alpha%29%2Asin%28beta%29+%2B+cos%28alpha%29%2Acos%28beta%29

of  Trigonometry  (see,  for example,  the lesson  Addition and subtraction formulas  in this site),  and the facts that

cos%28pi%2F6%29 = cos(30°) = sqrt%283%29%2F2   and   sin%28pi%2F6%29 = sin(30°) = 1%2F2.