1. Unit 7.4: Graphs of Polar Equations

2. Graph Points!

3. Graphs – constant graphs:
Graph each polar equation.
Constant distance r Constant direction ᶿ

4. Polar Express!
Typically, when we graph polar equations, we graph in radians
2𝜋 is approximately 6.28, whereas 360 𝑜 is, well, 360
Calculators can go through the values up to 6.28 a lot quicker than they can go through the values up to 360
We can recognize various types of polar graphs based on how the equation is written
Because you get to use the calculator, you might as well get to know how to recognize them using the calculator

5. What comes around
Circles are of the form 𝑟= acos 𝜃 or 𝑟= asin 𝜃

6. Lima
Limacons are of the form 𝑟=𝑎±𝑏 cos 𝜃 or 𝑟=𝑎±𝑏 𝑠𝑖𝑛𝜃, where a and b are both positive
Some have loops while others look like hearts

7. Lima
Some have dimples while others curve out like messed up circles

8. Roses are red
And of the form 𝑟= acos 𝑛𝜃 or 𝑟= asin 𝑛𝜃 , where 𝑛≥2 is an integer. n odd means n petals. n even means 2n petals.

9. Lemniscates
Are of the form 𝑟 2 = 𝑎 2 cos 2𝜃 or 𝑟 2 = 𝑎 2 sin 2𝜃

10. Spirals of Archimedes
Are of the form 𝑟=𝑎𝜃+𝑏

11. Graph the following in your calculator and determine which type of equation they are
𝑟=7 sin 𝜃
𝑟=3−6 cos 𝜃
𝑟=3 sin 2𝜃
𝑟=3− cos 𝜃
𝑟=7 cos 5𝜃
𝑟= sin 𝜃
𝑟 2 =9 cos 2𝜃
𝑟=3𝜃

12. By Hand!
Make a chart! ᶿ

13. Homework Assignment
Page 538 #22-28 Even, 32, 36, 38, 42, 44, 46
Below: Identify the type of graph:
Page 548 #4, 6, 10, 14, 18, 22, 26-33
Below: Answer as written:
Page 548 #34, 48a, 50-53