Thursday, January 1, 2015

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


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
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