What is the general solution for solvefor y,x=pi-arcsin(y) ?

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

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solvefor y,x=pi-arcsin(y)

solve for

y, x = π - arcsin (y)

y = sin (- x + π)

Solution steps

x = π - arcsin (y)

Switch sides

π - arcsin (y) = x

Move

π

to the right side

π - arcsin (y) = x

Subtract

π

from both sides

π - arcsin (y) - π = x - π

Simplify

- arcsin (y) = x - π

- arcsin (y) = x - π

Divide both sides by

- 1

- arcsin (y) = x - π

Divide both sides by

- 1

\frac{- arcsin ( y )}{- 1} = \frac{x}{- 1} - \frac{π}{- 1}

Simplify

\frac{- arcsin ( y )}{- 1} = \frac{x}{- 1} - \frac{π}{- 1}

Simplify

\frac{- arcsin ( y )}{- 1} : arcsin (y)

\frac{- arcsin ( y )}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{arcsin ( y )}{1}

Apply rule

\frac{a}{1} = a

= arcsin (y)

Simplify

\frac{x}{- 1} - \frac{π}{- 1} : - x + π

\frac{x}{- 1} - \frac{π}{- 1}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{x - π}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{x - π}{1}

Apply rule

\frac{a}{1} = a

= - (x - π)

Distribute parentheses

= - x - (- π)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - x + π

arcsin (y) = - x + π

arcsin (y) = - x + π

arcsin (y) = - x + π

Apply trig inverse properties

arcsin (y) = - x + π

arcsin (x) = a \Rightarrow x = sin (a)

y = sin (- x + π)

y = sin (- x + π)

arctan (x) = 3

tan (x) cos (x) = cos (x)

4 cos^{2} (θ) - 2 = - 1

sinh (x) = \frac{7}{24}, cosh (x)

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

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