What is the general solution for sin(1/2 x+pi/6)=(sqrt(3))/2 ?

The general solution for sin(1/2 x+pi/6)=(sqrt(3))/2 is x=4pin+pi/3 ,x=4pin+pi

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sin(1/2 x+pi/6)=(sqrt(3))/2

sin (\frac{1}{2} x + \frac{π}{6}) = \frac{3}{2}

x = 4 πn + \frac{π}{3}, x = 4 πn + π

Solution steps

sin (\frac{1}{2} x + \frac{π}{6}) = \frac{3}{2}

General solutions for

sin (\frac{1}{2} x + \frac{π}{6}) = \frac{3}{2}

\frac{1}{2} x + \frac{π}{6} = \frac{π}{3} + 2 πn, \frac{1}{2} x + \frac{π}{6} = \frac{2 π}{3} + 2 πn

Solve

\frac{1}{2} x + \frac{π}{6} = \frac{π}{3} + 2 πn : x = 4 πn + \frac{π}{3}

Solve

\frac{1}{2} x + \frac{π}{6} = \frac{2 π}{3} + 2 πn : x = 4 πn + π

x = 4 πn + \frac{π}{3}, x = 4 πn + π

6 sin (3 x) = 2

cos (x) \cdot sin (x) = 0

sin^{2} (θ) + 4 sin (θ) + 3 = 0

2 \cdot cos (x) = 0

3 sin (x) + 3 = 2 cos^{2} (x)

What is the general solution for sin(1/2 x+pi/6)=(sqrt(3))/2 ?
The general solution for sin(1/2 x+pi/6)=(sqrt(3))/2 is x=4pin+pi/3 ,x=4pin+pi