Precalculus Examples

$r \cos (θ) = 2$

Step 1

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

$\frac{r \cos (θ)}{\cos (θ)} = \frac{2}{\cos (θ)}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\cos (θ)$ .

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Step 2.1.1

Cancel the common factor.

$\frac{r \cos (θ)}{\cos (θ)} = \frac{2}{\cos (θ)}$

Step 2.1.2

Divide $r$ by $1$ .

$r = \frac{2}{\cos (θ)}$

Step 3

Simplify the right side.

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Step 3.1

Separate fractions.

$r = \frac{2}{1} \cdot \frac{1}{\cos (θ)}$

Step 3.2

Convert from $\frac{1}{\cos (θ)}$ to $\sec (θ)$ .

$r = \frac{2}{1} \sec (θ)$

Step 3.3

Divide $2$ by $1$ .

$r = 2 \sec (θ)$