What is the general solution for sin(4x)=-(sqrt(3))/2 ?

The general solution for sin(4x)=-(sqrt(3))/2 is x= pi/3+(pin)/2 ,x=(5pi}{12}+\frac{pin)/2

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sin(4x)=-(sqrt(3))/2

sin (4 x) = - \frac{3}{2}

x = \frac{π}{3} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

Solution steps

sin (4 x) = - \frac{3}{2}

General solutions for

sin (4 x) = - \frac{3}{2}

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

Solve

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

Solve

4 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

4 cot^{2} (3 x) - 12 csc (3 x) = - 12

cot (x - \frac{π}{2}) + 3 = 0

8 tan (θ) + 5 = 0

cos (\frac{θ}{2}) = \frac{2}{2}

cos (θ) = \frac{3}{2}

What is the general solution for sin(4x)=-(sqrt(3))/2 ?
The general solution for sin(4x)=-(sqrt(3))/2 is x= pi/3+(pin)/2 ,x=(5pi}{12}+\frac{pin)/2