What is the general solution for solvefor x,h=1+sin(pix) ?

The general solution for solvefor x,h=1+sin(pix) is x=(arcsin(h-1))/pi+2n,x=1+(arcsin(-h+1))/pi+2n

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solvefor x,h=1+sin(pix)

Solution

solve for

x, h = 1 + sin (π x)

Solution

x = \frac{arcsin ( h - 1 )}{π} + 2 n, x = 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

Solution steps

h = 1 + sin (π x)

Switch sides

1 + sin (π x) = h

Move

1

to the right side

1 + sin (π x) = h

Subtract

1

from both sides

1 + sin (π x) - 1 = h - 1

Simplify

sin (π x) = h - 1

sin (π x) = h - 1

Apply trig inverse properties

sin (π x) = h - 1

General solutions for

sin (π x) = h - 1

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

π x = arcsin (h - 1) + 2 πn, π x = π + arcsin (- h + 1) + 2 πn

π x = arcsin (h - 1) + 2 πn, π x = π + arcsin (- h + 1) + 2 πn

Solve

π x = arcsin (h - 1) + 2 πn : x = \frac{arcsin ( h - 1 )}{π} + 2 n

π x = arcsin (h - 1) + 2 πn

Divide both sides by

π

π x = arcsin (h - 1) + 2 πn

Divide both sides by

π

\frac{π x}{π} = \frac{arcsin ( h - 1 )}{π} + \frac{2 πn}{π}

Simplify

x = \frac{arcsin ( h - 1 )}{π} + 2 n

x = \frac{arcsin ( h - 1 )}{π} + 2 n

Solve

π x = π + arcsin (- h + 1) + 2 πn : x = 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

π x = π + arcsin (- h + 1) + 2 πn

Divide both sides by

π

π x = π + arcsin (- h + 1) + 2 πn

Divide both sides by

π

\frac{π x}{π} = \frac{π}{π} + \frac{arcsin ( - h + 1 )}{π} + \frac{2 πn}{π}

Simplify

\frac{π x}{π} = \frac{π}{π} + \frac{arcsin ( - h + 1 )}{π} + \frac{2 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{π}{π} + \frac{arcsin ( - h + 1 )}{π} + \frac{2 πn}{π} : 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

\frac{π}{π} + \frac{arcsin ( - h + 1 )}{π} + \frac{2 πn}{π}

Apply rule

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{arcsin ( - h + 1 )}{π} + \frac{2 πn}{π}

Cancel

\frac{2 πn}{π} : 2 n

\frac{2 πn}{π}

Cancel the common factor:

π

= 2 n

= 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

x = 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

x = 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

x = 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

x = \frac{arcsin ( h - 1 )}{π} + 2 n, x = 1 + \frac{arcsin ( - h + 1 )}{π} + 2 n

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,h=1+sin(pix) ?
The general solution for solvefor x,h=1+sin(pix) is x=(arcsin(h-1))/pi+2n,x=1+(arcsin(-h+1))/pi+2n