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

The general solution for sin(3x)=-(sqrt(3))/2 is x=(4pi)/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3

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

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

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

Solution steps

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

General solutions for

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

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

Solve

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

Solve

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

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

3 sin (2 x) sin (x) = 3 cos (x)

3 sin (x) + csc (x) = 0

cos (x) = \frac{4}{7}

csc^{2} (x) - 2 cot (x) = 0

tan (θ) = - \frac{4}{3}

What is the general solution for sin(3x)=-(sqrt(3))/2 ?
The general solution for sin(3x)=-(sqrt(3))/2 is x=(4pi)/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3