1. 13.1: Intro to Polar Equations

2. If you’re laying in bed staring at the ceiling and a fly lands on the ceiling, how can you describe where that fly is to someone else. You can measure the distance horizontally from one corner then measure the distance vertically to the fly.
This is called rectangular coordinates and it’s the method you have used to graph everything in math, UNTIL NOW!

3. Another method you could take is to measure the distance to the bug from the corner and the angle from the wall. This is called Polar Coordinates.
Today you’ll learn to convert between polar and rectangular coordinates and how to convert formulas between the two methods.

4. How to convert from Rectangular coordinates to Polar coordinates
𝑟= 𝑥 2 + 𝑦 2
𝜃= 𝑡𝑎𝑛 −1 ( 𝑦 𝑥 )
***Depending on quadrant you need to modify answer***

5. Convert the following rectangular coordinates to polar coordinates
(3,4)
(-2,5)

6. How to convert from Polar to Rectangular coordinates
𝑥=𝑟∙cos⁡(𝜃)
𝑦=𝑟∙sin⁡(𝜃)

7. Convert the following polar to rectangular coordinates
(2, 𝜋 6 )
(6, 5𝜋 3 )
Do part of the worksheet

8. How to convert from Rectangular to Polar formulas
1. Switch all x-values for 𝑥=𝑟∙cos⁡(𝜃)
2. Switch all y-values for 𝑦=𝑟∙sin⁡(𝜃)

9. Convert the following rectangular formulas to polar
𝑦=4𝑥−5
𝑦=3 𝑥 2

10. How to convert from Rectangular to Polar formulas
This isn’t going to be as easy as substitution because theta is so difficult to get rid of.
1. Try to put r-variable with cosine or sine. To convert rcos(𝜃) with x and rsin(𝜃) with y.

11. Convert the following polar formulas to rectangular
𝑟= −4 sin 𝜃 −2cos⁡(𝜃)
𝑟=3 sec 𝜃