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

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

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sin(A)= 1/2

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

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

Degrees

A = 3 0^{\circ} + 36 0^{\circ} n, A = 15 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{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn

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

- 4 sin^{2} (θ) - 3 sin (θ) + 5 = 0

cos^{2} (x) - sin^{2} (x) = - \frac{1}{2}

cos (θ) + 2 cos (θ + 24 0^{\circ}) = 1

arccos (x) = \frac{π}{8}

sin (θ) = 5

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