Precalculus Examples

$r \cos^{2} (θ) = \sin (θ)$

Step 1

Divide each term in $r \cos^{2} (θ) = \sin (θ)$ by $\cos^{2} (θ)$ .

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

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Cancel the common factor of $\cos^{2} (θ)$ .

Tap for more steps...

Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Divide $r$ by $1$ .

$r = \frac{\sin (θ)}{\cos^{2} (θ)}$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Factor $\cos (θ)$ out of $\cos^{2} (θ)$ .

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

Step 3.2

Separate fractions.

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

Step 3.3

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$r = \frac{1}{\cos (θ)} \tan (θ)$

Step 3.4

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

$r = \sec (θ) \tan (θ)$