What is the general solution for solvefor θ,sin(θ)= 1/2 ?

The general solution for solvefor θ,sin(θ)= 1/2 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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solvefor θ,sin(θ)= 1/2

solve for

θ, sin (θ) = \frac{1}{2}

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

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{1}{2}

General solutions for

sin (θ) = \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

sin (x + \frac{3 π}{2}) - cos^{2} (x) = 0

6 cos (x) - 6 sin (x) = 0

3 tan^{3} (x) - tan (x) = 0

5 sin (x) + 12 cos (x) = 13

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

What is the general solution for solvefor θ,sin(θ)= 1/2 ?
The general solution for solvefor θ,sin(θ)= 1/2 is θ= pi/6+2pin,θ=(5pi)/6+2pin