Unit 7.4: Graphs of Polar Equations

Graph Points!

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

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

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

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

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

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.

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

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

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=3.5+3.5 sin 𝜃 𝑟 2 =9 cos 2𝜃 𝑟=3𝜃

By Hand! Make a chart! ᶿ

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