What is the general solution for solvefor y,x=sin(y) ?

The general solution for solvefor y,x=sin(y) is y=arcsin(x)+2pin,y=pi+arcsin(-x)+2pin

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solvefor y,x=sin(y)

solve for

y, x = sin (y)

y = arcsin (x) + 2 πn, y = π + arcsin (- x) + 2 πn

Solution steps

x = sin (y)

Switch sides

sin (y) = x

Apply trig inverse properties

sin (y) = x

General solutions for

sin (y) = x

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

y = arcsin (x) + 2 πn, y = π + arcsin (- x) + 2 πn

y = arcsin (x) + 2 πn, y = π + arcsin (- x) + 2 πn

2 sin (\frac{x}{2}) + 3 = 0

2 cos^{2} (x) + 3 sin (x) = 0

tan (3 x) - 1 = 0

2 sin (2 x) - 1 = 0

sin (2 x) = \frac{2}{2}

What is the general solution for solvefor y,x=sin(y) ?
The general solution for solvefor y,x=sin(y) is y=arcsin(x)+2pin,y=pi+arcsin(-x)+2pin