1. 8.2.4 – Rewriting Polar Equations

2. We talked extensively about converting rectangular to polar equations
Use the substitutions;
x = rcos(ϴ)
y = rsin(ϴ)
x2 + y2 = r2
tan(ϴ) = y/x
Now, we will take something in terms or r and ϴ, and try to get back in terms of x and y

3. Conversion
In order to convert back to rectangular, we will need to try and isolate everything similar to the substitutions used before
IE, try and rewrite so we could possibly have an rcos(ϴ) or rsin(ϴ) in the equation

4. Key
Sometimes, if we are missing a particular factor, we may have to multiply both sides by a factor of r
Example. If I 2cos(ϴ) = 3r, if we multiply both sides by r, we would have 2rcos(ϴ) = 3r2

5. Example. Convert the equation r = 5cos(ϴ) from polar to rectangular.

6. Example. Convert the polar equation 2r = sec(ϴ) from polar to rectangular.

7. Example. Convert the polar equation ϴ = π/6 to rectangular.

8. Example. Convert the polar equation r = 7 from polar to rectangular
Example. Convert the polar equation r = 7 from polar to rectangular. (hint: think about squaring both sides)

9. Assignment
Pg. 629
31-40 all