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# 7.1: Polar Necessities

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Trigonometry, Chapter 6, Lesson 4.

## Plotting Coordinates & Exploring Polar Graphs

The coordinates of a polar curve are given as (θ, r)\begin{align*}(\theta, \ r)\end{align*}.

1. Plot and label the following points on the graph below: A(15, 4), B(270, 5), C(π6,3)\begin{align*}A(15^\circ, \ 4), \ B(270^\circ, \ 5), \ C \left( \frac{\pi}{6}, 3\right)\end{align*} and D(3π2,6)\begin{align*}D \left( \frac{3\pi}{2},6\right)\end{align*} .

2. If r(θ)=cos(θ)\begin{align*}r(\theta) = \cos(\theta)\end{align*}, what is r(π3)\begin{align*}r\left(\frac{\pi}{3}\right)\end{align*} ?

3. Graph r(θ)=22cos(θ)\begin{align*}r(\theta) = 2 - 2\cos(\theta)\end{align*}. What is the shape of the graph?

4. Using your graphing calculator, explore polar graphs by changing the equation from #3. Try to generate the graphs listed below. Which of the graphs were you able to make? Write the equation next to the graph shape.

• circle
• rose with even number of petals
• rose with odd number of petals
• limaçon with an inner loop

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