Trigonometry Examples

$y = - \sin (π x)$

Step 1

Rewrite the equation as $- \sin (π x) = y$ .

$- \sin (π x) = y$

Step 2

Divide each term in $- \sin (π x) = y$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \sin (π x) = y$ by $- 1$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2

Divide $\sin (π x)$ by $1$ .

$\sin (π x) = \frac{y}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$\sin (π x) = - 1 \cdot y$

Step 2.3.2

Rewrite $- 1 \cdot y$ as $- y$ .

$\sin (π x) = - y$

Step 3

Take the inverse sine of both sides of the equation to extract $x$ from inside the sine.

$π x = \arcsin (- y)$

Step 4

Divide each term in $π x = \arcsin (- y)$ by $π$ and simplify.

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Step 4.1

Divide each term in $π x = \arcsin (- y)$ by $π$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $π$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arcsin (- y)}{π}$