What is the general solution for -2=4sin(3x) ?

The general solution for -2=4sin(3x) is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3

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-2=4sin(3x)

- 2 = 4 sin (3 x)

x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Solution steps

- 2 = 4 sin (3 x)

Switch sides

4 sin (3 x) = - 2

Divide both sides by

4

sin (3 x) = - \frac{1}{2}

General solutions for

sin (3 x) = - \frac{1}{2}

3 x = \frac{7 π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

Solve

3 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

7 cos (x) = 3 + cos (x)

sin (t) = \frac{3}{4}

cos (2 θ) = \frac{- 3}{2}

cos (θ) = 0.65

- \frac{2}{3} sin (x) + \frac{1}{3} sin (2 x) = 0

What is the general solution for -2=4sin(3x) ?
The general solution for -2=4sin(3x) is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3