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

The general solution for sin(1/2 x+pi/3)=-1/2 is x=4pin+(5pi)/3 ,x=4pin+3pi

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sin(1/2 x+pi/3)=-1/2

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

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

Solution steps

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

General solutions for

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

\frac{1}{2} x + \frac{π}{3} = \frac{7 π}{6} + 2 πn, \frac{1}{2} x + \frac{π}{3} = \frac{11 π}{6} + 2 πn

Solve

\frac{1}{2} x + \frac{π}{3} = \frac{7 π}{6} + 2 πn : x = 4 πn + \frac{5 π}{3}

Solve

\frac{1}{2} x + \frac{π}{3} = \frac{11 π}{6} + 2 πn : x = 4 πn + 3 π

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

x, tan^{2} (x) = sec (x) - 1

csc^{2} (\frac{t}{2}) = 2

sin (2 x) = - \frac{1}{3}

- cos (3 x) = - cos (x)

2 sin (θ) cos (θ) - 2 cos (θ) = 0

What is the general solution for sin(1/2 x+pi/3)=-1/2 ?
The general solution for sin(1/2 x+pi/3)=-1/2 is x=4pin+(5pi)/3 ,x=4pin+3pi