Trigonometry Examples

$y = - 2 \sin (2 π x)$

Step 1

Rewrite the equation as $- 2 \sin (2 π x) = y$ .

$- 2 \sin (2 π x) = y$

Step 2

Divide each term in $- 2 \sin (2 π x) = y$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 \sin (2 π x) = y$ by $- 2$ .

$\frac{- 2 \sin (2 π x)}{- 2} = \frac{y}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 \sin (2 π x)}{- 2} = \frac{y}{- 2}$

Step 2.2.1.2

Divide $\sin (2 π x)$ by $1$ .

$\sin (2 π x) = \frac{y}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$\sin (2 π x) = - \frac{y}{2}$

Step 3

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

$2 π x = \arcsin (- \frac{y}{2})$

Step 4

Divide each term in $2 π x = \arcsin (- \frac{y}{2})$ by $2 π$ and simplify.

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Step 4.1

Divide each term in $2 π x = \arcsin (- \frac{y}{2})$ by $2 π$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Rewrite the expression.

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

Step 4.2.2

Cancel the common factor of $π$ .

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Step 4.2.2.1

Cancel the common factor.

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

Step 4.2.2.2

Divide $x$ by $1$ .

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