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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 $(\theta, \ r)$.

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

2. If $r(\theta) = \cos(\theta)$, what is $r\left(\frac{\pi}{3}\right)$ ?

3. Graph $r(\theta) = 2 - 2\cos(\theta)$. 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

Feb 23, 2012

Nov 04, 2014