What is the general solution for sin(x)= 1/2 ,0<x< pi/2 ?

The general solution for sin(x)= 1/2 ,0<x< pi/2 is x= pi/6

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sin(x)= 1/2 ,0<x< pi/2

sin (x) = \frac{1}{2}, 0 < x < \frac{π}{2}

x = \frac{π}{6}

Degrees

x = 3 0^{\circ}

Solution steps

sin (x) = \frac{1}{2}, 0 < x < \frac{π}{2}

General solutions for

sin (x) = \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}

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

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

Solutions for the range

0 < x < \frac{π}{2}

x = \frac{π}{6}

sin (2 x) = cos (8 x)

8 = sin (x)

arctan (4 x) + arctan (6 x) = - \frac{π}{2}

- 2 cot (x) + csc^{2} (x) = 0

sin (3 x + \frac{π}{4}) = \frac{3}{2}

What is the general solution for sin(x)= 1/2 ,0<x< pi/2 ?
The general solution for sin(x)= 1/2 ,0<x< pi/2 is x= pi/6