Precalculus Examples

$r = 2 \sin (θ)$

Step 1

Rewrite the equation as $2 \sin (θ) = r$ .

$2 \sin (θ) = r$

Step 2

Divide each term in $2 \sin (θ) = r$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 \sin (θ) = r$ by $2$ .

$\frac{2 \sin (θ)}{2} = \frac{r}{2}$

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.

$\frac{2 \sin (θ)}{2} = \frac{r}{2}$

Step 2.2.1.2

Divide $\sin (θ)$ by $1$ .

$\sin (θ) = \frac{r}{2}$

Step 3

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

$θ = \arcsin (\frac{r}{2})$

Step 4

To rewrite as a function of $r$ , write the equation so that $θ$ is by itself on one side of the equal sign and an expression involving only $r$ is on the other side.

$f (r) = \arcsin (\frac{r}{2})$