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

The general solution for 2sin(1/2 x)-1=0 is x= pi/3+4pin,x=(5pi)/3+4pin

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

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

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

Solution steps

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

Move

1

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{1}{2} x = \frac{π}{6} + 2 πn, \frac{1}{2} x = \frac{5 π}{6} + 2 πn

Solve

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

Solve

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

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

sin (θ) = \frac{1}{3}, 0 < θ < \frac{π}{2}

sec^{2} (x) + 2 sec (x) = 0

3 tan (\frac{θ + 11 π}{6}) = 3

8 cos^{2} (θ) + 13 = 14 cos (θ) + 8

cos (3 x) = - \frac{1}{2}, 0 \leq x < 2 π

What is the general solution for 2sin(1/2 x)-1=0 ?
The general solution for 2sin(1/2 x)-1=0 is x= pi/3+4pin,x=(5pi)/3+4pin