CPM Homework Help : PC Problem 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.
challenge problem

Step 1:

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

Note: Steps can be done in various orders.

Step 2:

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

Step 3:

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

Step 4:

Multiply both sides by $r$ .

Step 5:

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

Step 6:

Simplify.