Trigonometry Examples

y = sin (π x)

$y = \sin (π x)$

Step 1

Rewrite the equation as

sin (π x) = y

$\sin (π x) = y$ .

sin (π x) = y

$\sin (π x) = y$

Step 2

Take the inverse sine of both sides of the equation to extract

x

$x$ from inside the sine.

π x = arcsin (y)

$π x = \arcsin (y)$

Step 3

Divide each term in

π x = arcsin (y)

$π x = \arcsin (y)$ by

π

$π$ and simplify.

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Step 3.1

Divide each term in

π x = arcsin (y)

$π x = \arcsin (y)$ by

π

$π$ .

\frac{π x}{π} = \frac{arcsin (y)}{π}

$\frac{π x}{π} = \frac{\arcsin (y)}{π}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

π

$π$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{π x}{π} = \frac{\arcsin (y)}{π}$

Step 3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{\arcsin (y)}{π}$

$y = \sin (π x)$

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