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

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

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

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

x = π + 6 πn, x = 2 π + 6 πn

Solution steps

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

General solutions for

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

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

Solve

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

Solve

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

x = π + 6 πn, x = 2 π + 6 πn

2 cos (θ) sin (θ) - cos (θ) = 0

- sin (x) = cos (2 x)

2 sin (2 (x - \frac{π}{3})) = - 3

- 6 sin (x) - 6 cos (x) = 0

sin (4 x) - sin (2 x) = cos (3 x)

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