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

The general solution for solvefor x,y=sin((pix)/2) is x=(2arcsin(y))/pi+4n,x=2+(2arcsin(-y))/pi+4n

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Popular >

solvefor x,y=sin((pix)/2)

Solution

solve for

x, y = sin (\frac{π x}{2})

Solution

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

Solution steps

y = sin (\frac{π x}{2})

Switch sides

sin (\frac{π x}{2}) = y

Apply trig inverse properties

sin (\frac{π x}{2}) = y

General solutions for

sin (\frac{π x}{2}) = y

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

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

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

Solve

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

\frac{π x}{2} = arcsin (y) + 2 πn

Multiply both sides by

2

\frac{π x}{2} = arcsin (y) + 2 πn

Multiply both sides by

2

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

Simplify

π x = 2 arcsin (y) + 4 πn

π x = 2 arcsin (y) + 4 πn

Divide both sides by

π

π x = 2 arcsin (y) + 4 πn

Divide both sides by

π

\frac{π x}{π} = \frac{2 arcsin ( y )}{π} + \frac{4 πn}{π}

Simplify

x = \frac{2 arcsin ( y )}{π} + 4 n

x = \frac{2 arcsin ( y )}{π} + 4 n

Solve

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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

π x = 2 π + 2 arcsin (- y) + 4 πn

π x = 2 π + 2 arcsin (- y) + 4 πn

Divide both sides by

π

π x = 2 π + 2 arcsin (- y) + 4 πn

Divide both sides by

π

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

Simplify

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

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

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

\frac{2 π}{π} + \frac{2 arcsin ( - y )}{π} + \frac{4 πn}{π}

Cancel

\frac{2 π}{π} : 2

\frac{2 π}{π}

Cancel the common factor:

π

= 2

= 2 + \frac{2 arcsin ( - y )}{π} + \frac{4 πn}{π}

Cancel

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Cancel the common factor:

π

= 4 n

= 2 + \frac{2 arcsin ( - y )}{π} + 4 n

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

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

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

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

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,y=sin((pix)/2) ?
The general solution for solvefor x,y=sin((pix)/2) is x=(2arcsin(y))/pi+4n,x=2+(2arcsin(-y))/pi+4n