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).
1. Plot and label the following points on the graph below: A(15∘, 4), B(270∘, 5), C(π6,3) and D(3π2,6) .
2. If r(θ)=cos(θ), what is r(π3) ?
3. Graph r(θ)=2−2cos(θ). 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.
- rose with even number of petals
- rose with odd number of petals
- limaçon with an inner loop