What is the general solution for 2sin(1/2 x)-sqrt(3)=0 ?

The general solution for 2sin(1/2 x)-sqrt(3)=0 is x=(2pi)/3+4pin,x=(4pi)/3+4pin

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2sin(1/2 x)-sqrt(3)=0

2 sin (\frac{1}{2} x) - 3 = 0

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

Solution steps

2 sin (\frac{1}{2} x) - 3 = 0

Move

3

to the right side

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

Divide both sides by

2

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

General solutions for

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

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

Solve

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

Solve

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

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

sin (2 θ) = 2 cos (θ)

30 = 30 cos (\frac{1}{4} (x - 5)) + 15

sec (x) sin^{2} (x) = sec (x)

cos (θ) = - 0.07

cos (θ) = - 0.29

What is the general solution for 2sin(1/2 x)-sqrt(3)=0 ?
The general solution for 2sin(1/2 x)-sqrt(3)=0 is x=(2pi)/3+4pin,x=(4pi)/3+4pin