What is the general solution for sin(θ)=0.5 ?

The general solution for sin(θ)=0.5 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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sin(θ)=0.5

sin (θ) = 0.5

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) = 0.5

General solutions for

sin (θ) = 0.5

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

3 + tan (2 x) = 0

csc (2 x) = 2

tan (x) = \frac{3}{3}

6 (1 - cos (θ)) = sin^{2} (θ)

25 tan^{2} (θ) - 9 = 0

What is the general solution for sin(θ)=0.5 ?
The general solution for sin(θ)=0.5 is θ= pi/6+2pin,θ=(5pi)/6+2pin