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

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

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sin(α)= 1/2

sin (α) = \frac{1}{2}

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

Degrees

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

Solution steps

sin (α) = \frac{1}{2}

General solutions for

sin (α) = \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}

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

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

3 sin (3 x) + 3 cos (3 x) = 0

tan (θ) = - \frac{4}{5}, \frac{π}{2} < θ < π

cos (2 x) = sin (x), 0 \leq x < 2 π

θ, x = sec (θ)

sin (x) + cos (x) = - 1, 0 \leq x \leq 2 π

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