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

The general solution for sin(y)=-1/2 is y=(7pi)/6+2pin,y=(11pi)/6+2pin

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sin(y)=-1/2

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

y = \frac{7 π}{6} + 2 πn, y = \frac{11 π}{6} + 2 πn

Degrees

y = 21 0^{\circ} + 36 0^{\circ} n, y = 33 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{7 π}{6} + 2 πn, y = \frac{11 π}{6} + 2 πn

y = \frac{7 π}{6} + 2 πn, y = \frac{11 π}{6} + 2 πn

cos^{22} (x) - 2 sin^{2} (x) - 1 = 0

tan (θ) = \frac{3 5}{2}

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

3 sin^{2} (x) - sin (x) - 4 = 0

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

What is the general solution for sin(y)=-1/2 ?
The general solution for sin(y)=-1/2 is y=(7pi)/6+2pin,y=(11pi)/6+2pin