Write as a Function of r r=6cos(theta)

$r = 6 \cos (θ)$

Step 1

Rewrite the equation as $6 \cos (θ) = r$ .

$6 \cos (θ) = r$

Step 2

Divide each term in $6 \cos (θ) = r$ by $6$ and simplify.

Divide each term in $6 \cos (θ) = r$ by $6$ .

$\frac{6 \cos (θ)}{6} = \frac{r}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 \cos (θ)}{6} = \frac{r}{6}$

Divide $\cos (θ)$ by $1$ .

$\cos (θ) = \frac{r}{6}$

Step 3

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

$θ = \arccos (\frac{r}{6})$

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.

$f (r) = \arccos (\frac{r}{6})$

Write as a Function of r r=6cos(theta)

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