What is the general solution for solvefor y,x=2sin(y) ?

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

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solvefor y,x=2sin(y)

solve for

y, x = 2 sin (y)

y = arcsin (\frac{x}{2}) + 2 πn, y = π + arcsin (- \frac{x}{2}) + 2 πn

Solution steps

x = 2 sin (y)

Switch sides

2 sin (y) = x

Divide both sides by

2

2 sin (y) = x

Divide both sides by

2

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

y = arcsin (\frac{x}{2}) + 2 πn, y = π + arcsin (- \frac{x}{2}) + 2 πn

y = arcsin (\frac{x}{2}) + 2 πn, y = π + arcsin (- \frac{x}{2}) + 2 πn

2 sin (2 x) + 2 sin (x) = 1 + 2 cos (x)

3 sin (x) + 2 = 0

cos (φ) = 0.71

sin (θ) + 1 = 1

7 sin (x) cos (x) + 3 cos (x) = 0

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