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

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

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2sqrt(3)sin(θ/2)=3

23 sin (\frac{θ}{2}) = 3

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

Solution steps

23 sin (\frac{θ}{2}) = 3

Divide both sides by

23

sin (\frac{θ}{2}) = \frac{3}{2}

General solutions for

sin (\frac{θ}{2}) = \frac{3}{2}

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

Solve

\frac{θ}{2} = \frac{π}{3} + 2 πn : θ = \frac{2 π}{3} + 4 πn

Solve

\frac{θ}{2} = \frac{2 π}{3} + 2 πn : θ = \frac{4 π}{3} + 4 πn

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

tan (θ) = - \frac{1}{7}

2 sin (x) = \frac{4 cos ( x ) - 1}{tan ( x )}

6 cos (5 x) = 3

2 sin (2 θ) cos (θ) + cos (2 θ) sin (θ) = 0

sin (x) = cos^{2} (x) - sin^{2} (x)

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