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

The general solution for sin(x/4)=(-sqrt(3))/2 is x=(16pi)/3+8pin,x=(20pi)/3+8pin

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

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

x = \frac{16 π}{3} + 8 πn, x = \frac{20 π}{3} + 8 πn

Solution steps

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

Apply the fraction rule:

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

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

General solutions for

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

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

Solve

\frac{x}{4} = \frac{4 π}{3} + 2 πn : x = \frac{16 π}{3} + 8 πn

Solve

\frac{x}{4} = \frac{5 π}{3} + 2 πn : x = \frac{20 π}{3} + 8 πn

x = \frac{16 π}{3} + 8 πn, x = \frac{20 π}{3} + 8 πn

2 sin (x) cos (x) = \frac{2}{2}

arctan (x) = 90

cos (5 θ) - cos (7 θ) = 0

sin (x - \frac{π}{3}) = \frac{2}{2}

5 cos (a) + 4 = 0

What is the general solution for sin(x/4)=(-sqrt(3))/2 ?
The general solution for sin(x/4)=(-sqrt(3))/2 is x=(16pi)/3+8pin,x=(20pi)/3+8pin