SOLUTION: Solve for all solution: sin(3x)cos(6x)-cos(3x)sin(6x)=-0.9

Algebra ->  Trigonometry-basics -> SOLUTION: Solve for all solution: sin(3x)cos(6x)-cos(3x)sin(6x)=-0.9      Log On


   

Question 935775: Solve for all solution:
sin(3x)cos(6x)-cos(3x)sin(6x)=-0.9
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
use angle subtraction identity to get
sin%283x-6x%29=-0.9
then since sine is an odd function

-sin%283x%29=-0.9

which leads to

sin%283x%29=0.9

arscin%28sin%283x%29%29=arcsin%280.9%29
3x=arcsin%280.9%29%2B2%2Api%2An

x=%282%2Api%2An%2Barcsin%280.9%29%29%2F3