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}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

5 sin (3 x) - 11 = 3 sin (3 x) - 12

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

8 - 8 sin (x) = 5 cos^{2} (x)

0 = - \frac{9 π ^{2}}{3200} cos (\frac{π x}{80})

cos^{2} (a) + 2 sin (a) + 1 = 0

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