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

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

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sin(B)= 1/2

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

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

Degrees

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

Solution steps

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

General solutions for

sin (B) = \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}

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

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

- 9 cos (x) = 4

arcsin (3 x) + arcsin (x) = 6 0^{\circ}

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

4 cos^{2} (2 x) - 4 cos (2 x) + 1 = 0

cos (θ) = \frac{2}{13}

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