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

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

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

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

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

Solution steps

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

Apply the fraction rule:

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

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

General solutions for

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

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

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

sec (θ) = 2

2 cos^{2} (θ) - 3 cos (θ) + 1 = 0

cos (2 θ) = 1

sec^{2} (x) = 1

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