### Home > PC > Chapter 11 > Lesson 11.1.3 > Problem11-46

11-46.

In problem 11-40 you found that the polar equation $\frac { \operatorname { sin } ( \theta + \frac { \pi } { 4 } ) } { \operatorname { cos } ^ { 2 } ( \theta + \frac { \pi } { 4 } ) }$ will generate a parabola that is rotated $45°$ clockwise. Convert the equation into rectangular form.

Multiply both sides by $\cos^2\left(θ + \frac{π}{4}\right)$.

Note: Steps can be done in various orders.

Expand $\sin\left(θ + \frac{π}{4}\right)$ and $\cos\left(θ + \frac{π}{4}\right)$ using the angle sum identities.

Change $\sin\left( \frac{π}{4}\right)$ and$\cos\left(\frac{π}{4}\right)$ to their numeric values.

Multiply both sides by $r$.

Substitute $x$ for $r \cos\left(θ\right)$, etc.

Simplify.