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Solve the following equation for all solutions: sin(6x)cos(11x)-cos(6x)sin(11x)=-.1

1 answer

Recall that sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
Thus,
sin(6x)cos(11x) - cos(6x)sin(11x) = -0.1
sin(6x - 11x) = -0.1
sin(-5x) = -0.1
-sin(5x) = -0.1
sin(5x) = 0.1
5x = sin^-1 (0.1)
x = [ sin^-1 (0.1) ] / 5
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