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Popular >

solvefor y=1+sin((pix)/4),x

Solution

solve for

y = 1 + sin (\frac{π x}{4}), x

Solution

x = \frac{4 arcsin ( y - 1 )}{π} + 8 n, x = 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

Solution steps

y = 1 + sin (\frac{π x}{4})

Switch sides

1 + sin (\frac{π x}{4}) = y

Move

1

to the right side

1 + sin (\frac{π x}{4}) = y

Subtract

1

from both sides

1 + sin (\frac{π x}{4}) - 1 = y - 1

Simplify

sin (\frac{π x}{4}) = y - 1

sin (\frac{π x}{4}) = y - 1

Apply trig inverse properties

sin (\frac{π x}{4}) = y - 1

General solutions for

sin (\frac{π x}{4}) = y - 1

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

\frac{π x}{4} = arcsin (y - 1) + 2 πn, \frac{π x}{4} = π + arcsin (- y + 1) + 2 πn

\frac{π x}{4} = arcsin (y - 1) + 2 πn, \frac{π x}{4} = π + arcsin (- y + 1) + 2 πn

Solve

\frac{π x}{4} = arcsin (y - 1) + 2 πn : x = \frac{4 arcsin ( y - 1 )}{π} + 8 n

\frac{π x}{4} = arcsin (y - 1) + 2 πn

Multiply both sides by

4

\frac{π x}{4} = arcsin (y - 1) + 2 πn

Multiply both sides by

4

\frac{4 π x}{4} = 4 arcsin (y - 1) + 4 \cdot 2 πn

Simplify

π x = 4 arcsin (y - 1) + 8 πn

π x = 4 arcsin (y - 1) + 8 πn

Divide both sides by

π

π x = 4 arcsin (y - 1) + 8 πn

Divide both sides by

π

\frac{π x}{π} = \frac{4 arcsin ( y - 1 )}{π} + \frac{8 πn}{π}

Simplify

x = \frac{4 arcsin ( y - 1 )}{π} + 8 n

x = \frac{4 arcsin ( y - 1 )}{π} + 8 n

Solve

\frac{π x}{4} = π + arcsin (- y + 1) + 2 πn : x = 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

\frac{π x}{4} = π + arcsin (- y + 1) + 2 πn

Multiply both sides by

4

\frac{π x}{4} = π + arcsin (- y + 1) + 2 πn

Multiply both sides by

4

\frac{4 π x}{4} = 4 π + 4 arcsin (- y + 1) + 4 \cdot 2 πn

Simplify

π x = 4 π + 4 arcsin (- y + 1) + 8 πn

π x = 4 π + 4 arcsin (- y + 1) + 8 πn

Divide both sides by

π

π x = 4 π + 4 arcsin (- y + 1) + 8 πn

Divide both sides by

π

\frac{π x}{π} = \frac{4 π}{π} + \frac{4 arcsin ( - y + 1 )}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} = \frac{4 π}{π} + \frac{4 arcsin ( - y + 1 )}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{4 π}{π} + \frac{4 arcsin ( - y + 1 )}{π} + \frac{8 πn}{π} : 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

\frac{4 π}{π} + \frac{4 arcsin ( - y + 1 )}{π} + \frac{8 πn}{π}

Cancel

\frac{4 π}{π} : 4

\frac{4 π}{π}

Cancel the common factor:

π

= 4

= 4 + \frac{4 arcsin ( - y + 1 )}{π} + \frac{8 πn}{π}

Cancel

\frac{8 πn}{π} : 8 n

\frac{8 πn}{π}

Cancel the common factor:

π

= 8 n

= 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

x = 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

x = 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

x = 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

x = \frac{4 arcsin ( y - 1 )}{π} + 8 n, x = 4 + \frac{4 arcsin ( - y + 1 )}{π} + 8 n

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