What is the general solution for 2sin(3x)=-1 ?

The general solution for 2sin(3x)=-1 is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3

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2sin(3x)=-1

2 sin (3 x) = - 1

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

Solution steps

2 sin (3 x) = - 1

Divide both sides by

2

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}

8 sin^{2} (θ) + 2 sin (θ) - 1 = 0

tan (θ) = 6

sin (4 x) = \frac{1}{2}

cos (x) - sin (x) = 0, 0 \leq x < 2 π

x, y = sin (\frac{π x}{2})

What is the general solution for 2sin(3x)=-1 ?
The general solution for 2sin(3x)=-1 is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3