SOLUTION: Write the expression in terms of sine only. {{{3sin(8 pi X)+ 3 sqrt(3)cos(8 pi X)}}} I missed a day in class and I'm just not sure how to do this. I looked in the book, but that

Algebra ->  Trigonometry-basics -> SOLUTION: Write the expression in terms of sine only. {{{3sin(8 pi X)+ 3 sqrt(3)cos(8 pi X)}}} I missed a day in class and I'm just not sure how to do this. I looked in the book, but that      Log On


   

Question 868857: Write the expression in terms of sine only.
3sin%288+pi+X%29%2B+3+sqrt%283%29cos%288+pi+X%29
I missed a day in class and I'm just not sure how to do this. I looked in the book, but that really doesn't help without a little outside information. Thanks!

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
3sin%288+pi+X%29%2B+3+sqrt%283%29cos%288+pi+X%29

3sin%288+pi+X%29=-+3+sqrt%283%29cos%288+pi+X%29
square both sides
+9sin%5E2%288piX%29=27cos%5E2%288piX%29+
/27
+%289%2F27%29sin%5E2%288piX%29=cos%5E2%288piX%29+
+%289%2F27%29sin%5E2%288piX%29=1-sin%5E2%288piX%29+
+%281%2F3%29sin%5E2%288piX%29%2Bsin%5E2%288piX%29=1+
+%284%2F3%29sin%5E2%288piX%29=1+
sin^2(8piX) =3/4
sin+%288piX%29+=sqrt%283%29%2F2