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

The general solution for sin(y)=sqrt(1/2) is y= pi/4+2pin,y=(3pi)/4+2pin

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sin(y)=sqrt(1/2)

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

y = \frac{π}{4} + 2 πn, y = \frac{3 π}{4} + 2 πn

Degrees

y = 4 5^{\circ} + 36 0^{\circ} n, y = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

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{π}{4} + 2 πn, y = \frac{3 π}{4} + 2 πn

y = \frac{π}{4} + 2 πn, y = \frac{3 π}{4} + 2 πn

tan (2 θ) = 2.93

cot (θ + 1) csc (θ - 1) = 0

sin (a) = 0.9455

x, \frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}

2 - 2 sin^{2} (x) = 0

What is the general solution for sin(y)=sqrt(1/2) ?
The general solution for sin(y)=sqrt(1/2) is y= pi/4+2pin,y=(3pi)/4+2pin