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

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

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sin(3θ)=-(sqrt(3))/2

sin (3 θ) = - \frac{3}{2}

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

Solution steps

sin (3 θ) = - \frac{3}{2}

General solutions for

sin (3 θ) = - \frac{3}{2}

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

Solve

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

Solve

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

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

x, arctan (\frac{y}{x}) = 0

cos (x) = - 1, 0 \leq x < 2 π

2 cos^{2} (x) - 3 sin (x) - 2 = 0

4 sin (x) cos^{2} (x) = cos (x)

cos (x) = 3 sin (x)

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