Trigonometry Examples

$y = - 3 \sin (\frac{1}{2} x)$

Step 1

Rewrite the equation as $- 3 \sin (\frac{1}{2} x) = y$ .

$- 3 \sin (\frac{1}{2} x) = y$

Step 2

Divide each term in $- 3 \sin (\frac{1}{2} x) = y$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 \sin (\frac{1}{2} x) = y$ by $- 3$ .

$\frac{- 3 \sin (\frac{1}{2} x)}{- 3} = \frac{y}{- 3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 \sin (\frac{1}{2} x)}{- 3} = \frac{y}{- 3}$

Step 2.2.1.2

Divide $\sin (\frac{1}{2} x)$ by $1$ .

$\sin (\frac{1}{2} x) = \frac{y}{- 3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$\sin (\frac{1}{2} x) = - \frac{y}{3}$

Step 3

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

$\frac{1}{2} x = \arcsin (- \frac{y}{3})$

Step 4

Simplify the left side.

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Step 4.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} = \arcsin (- \frac{y}{3})$

Step 5

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \arcsin (- \frac{y}{3})$

Step 6

Simplify the left side.

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Step 6.1

Cancel the common factor of $2$ .

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Step 6.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \arcsin (- \frac{y}{3})$

Step 6.1.2

Rewrite the expression.

$x = 2 \arcsin (- \frac{y}{3})$