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

The general solution for sin(3x-(2pi)/3)=-1/2 is x=(2pin)/3+(11pi}{18},x=\frac{2pin)/3+(5pi)/6

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sin(3x-(2pi)/3)=-1/2

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

x = \frac{2 πn}{3} + \frac{11 π}{18}, x = \frac{2 πn}{3} + \frac{5 π}{6}

Solution steps

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

General solutions for

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

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

Solve

3 x - \frac{2 π}{3} = \frac{7 π}{6} + 2 πn : x = \frac{2 πn}{3} + \frac{11 π}{18}

Solve

3 x - \frac{2 π}{3} = \frac{11 π}{6} + 2 πn : x = \frac{2 πn}{3} + \frac{5 π}{6}

x = \frac{2 πn}{3} + \frac{11 π}{18}, x = \frac{2 πn}{3} + \frac{5 π}{6}

1 - cos (θ) = 1

csc^{2} (x) + 2 cot (x) = 1

2 cos (x) + sin (x) = 2

sin (θ) tan (θ) - sin (θ) = 0

6 cos^{2} (x) + 5 sin (x) = 7

What is the general solution for sin(3x-(2pi)/3)=-1/2 ?
The general solution for sin(3x-(2pi)/3)=-1/2 is x=(2pin)/3+(11pi}{18},x=\frac{2pin)/3+(5pi)/6