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

The general solution for sin(θ)= 1/2 ,θ is No Solution for θ\in\mathbb{R}

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sin(θ)= 1/2 ,θ

sin (θ) = \frac{1}{2}, θ

No Solution for θ \in R

Solution steps

sin (θ) = \frac{1}{2}, θ

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

Solutions for the range

θ

No Solution for θ \in R

tan (x) = \frac{40}{34}

cot (b) = - 5

sin^{2} (x) - cos^{3} (x) = 0

1 = cot (θ)

arccos (2 x) = 0

What is the general solution for sin(θ)= 1/2 ,θ ?
The general solution for sin(θ)= 1/2 ,θ is No Solution for θ\in\mathbb{R}