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

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

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sin(y)= 1/2

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

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

Degrees

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

Solution steps

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

General solutions for

sin (y) = \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}

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

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

3 sin^{2} (x) = 5 sin (x) + 2

sin (x) + cos (x) = 0, - \frac{π}{2} \leq x \leq π

sin (x) = \frac{7}{4}

2 tan^{2} (x) + 9 tan (x) + 3 = 0

sin^{2} (x) = (\frac{2 m - 4}{5})

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