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

The general solution for 2sin(3x-pi/3)=-sqrt(3) is x=(2pin)/3+(5pi)/9 ,x=(2pin)/3+(2pi)/3

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

2 sin (3 x - \frac{π}{3}) = - 3

x = \frac{2 πn}{3} + \frac{5 π}{9}, x = \frac{2 πn}{3} + \frac{2 π}{3}

Solution steps

2 sin (3 x - \frac{π}{3}) = - 3

Divide both sides by

2

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

General solutions for

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

3 x - \frac{π}{3} = \frac{4 π}{3} + 2 πn, 3 x - \frac{π}{3} = \frac{5 π}{3} + 2 πn

Solve

3 x - \frac{π}{3} = \frac{4 π}{3} + 2 πn : x = \frac{2 πn}{3} + \frac{5 π}{9}

Solve

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

x = \frac{2 πn}{3} + \frac{5 π}{9}, x = \frac{2 πn}{3} + \frac{2 π}{3}

2 cos (2 x - \frac{π}{2}) = 3

cos (2 x) - 2 sin^{2} (x) = 0

3 - 2 cot^{2} (x) = - cot^{2} (x)

2 cos (t) + 1 = 0

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

What is the general solution for 2sin(3x-pi/3)=-sqrt(3) ?
The general solution for 2sin(3x-pi/3)=-sqrt(3) is x=(2pin)/3+(5pi)/9 ,x=(2pin)/3+(2pi)/3