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

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

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sin(a)=-1/2

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

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

Degrees

a = 21 0^{\circ} + 36 0^{\circ} n, a = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

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

General solutions for

sin (a) = - \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}

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

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

tan (a) + sec (a) = 2

sin (θ) = \frac{5}{11}

4 = - 8 cos (θ)

2 cos^{2} (θ) - 5 cos (θ) = 3

12 sin^{2} (x) - 20 sin (x) = - 8

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