Question

Sin (3x)cos(6x) - cos (3x) sin(6x)=-0.9

Answer 1

Explanation:

sin(3x)cos(6x)-cos(3x)sin (6x)=-0.9

sina cos b-cos asin b=sin(a-b)

sin(3x-6x)=-0.9

sin(-3x)=-0.9

-sin (3x)=-0.9

sin (3x)=0.9

3x=arcsin (0.9)≈64.16°,115.84°

3x=360n+64.16,360n+115.84

x=120 n+21.39°,120 n+38.61°

Answer 2

x=21.38602241

Explanation:

Given: sin(3x)cos(6x) - cos(3x)sin(6x) = -0.9

Rewrite as difference identity: sin(3x-6x)=-0.9

Combine like terms in parentheses: sin(-3x)=-0.9

Take the inverse sine of both sides: -3x=-64.15806724

Divide both sides by -3: x=21.38602241

Refer to the sheet to see all trigonometric identities