What is the general solution for solvefor y,x=5*sin(sqrt(y)) ?

The general solution for solvefor y,x=5*sin(sqrt(y)) is

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solvefor y,x=5*sin(sqrt(y))

solve for

y, x = 5 \cdot sin (y)

y = arcsin^{2} (\frac{x}{5}) + 4 πn arcsin (\frac{x}{5}) + 4 π^{2} n^{2}, y = π^{2} + 4 π^{2} n + 4 π^{2} n^{2} + 2 π arcsin (- \frac{x}{5}) + 4 πn arcsin (- \frac{x}{5}) + arcsin^{2} (- \frac{x}{5})

Solution steps

x = 5 sin (y)

Switch sides

5 sin (y) = x

Divide both sides by

5

sin (y) = \frac{x}{5}

Apply trig inverse properties

y = arcsin (\frac{x}{5}) + 2 πn, y = π + arcsin (- \frac{x}{5}) + 2 πn

Solve

y = arcsin (\frac{x}{5}) + 2 πn : y = arcsin^{2} (\frac{x}{5}) + 4 πn arcsin (\frac{x}{5}) + 4 π^{2} n^{2}

Solve

y = π + arcsin (- \frac{x}{5}) + 2 πn : y = π^{2} + 4 π^{2} n + 4 π^{2} n^{2} + 2 π arcsin (- \frac{x}{5}) + 4 πn arcsin (- \frac{x}{5}) + arcsin^{2} (- \frac{x}{5})

y = arcsin^{2} (\frac{x}{5}) + 4 πn arcsin (\frac{x}{5}) + 4 π^{2} n^{2}, y = π^{2} + 4 π^{2} n + 4 π^{2} n^{2} + 2 π arcsin (- \frac{x}{5}) + 4 πn arcsin (- \frac{x}{5}) + arcsin^{2} (- \frac{x}{5})

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

t, x = a cos^{2} (t) + b sin^{2} (t)

cos (3 x) - sin (3 x) = 0

cos (x) = 0.1885

8 sin^{2} (x) cos^{2} (x) = 1

What is the general solution for solvefor y,x=5*sin(sqrt(y)) ?
The general solution for solvefor y,x=5*sin(sqrt(y)) is