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

The general solution for sin(2x)=(-sqrt(3))/2 is x=(2pi)/3+pin,x=(5pi)/6+pin

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

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

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

Solution steps

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

General solutions for

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

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

Solve

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

Solve

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

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

cos (2 θ) - cos (θ) = 0

cot (x) + 3 = 0

4 sin^{2} (θ) + 4 = 5

sec^{2} (x) - 6 tan (x) = - 4

64 cos^{2} (x) - 16 = 0

What is the general solution for sin(2x)=(-sqrt(3))/2 ?
The general solution for sin(2x)=(-sqrt(3))/2 is x=(2pi)/3+pin,x=(5pi)/6+pin