1. Objective: Graph and analyze rose curves. Warm up 1.Plot point. a.Find point symmetric w.r.t. polar axis. b.Find point symmetric w.r.t.. c.Find point symmetric w.r.t. the pole.

2. 2.Test for symmetry w.r.t. a.Polar axis. b.Line. c.Pole.

3. Investigation: Rose Curves With your grapher in polar mode enter: 1. Set = 0; = 0.13 and graph r on your calculator using the given value for. a. b. c. d. 2.Describe in writing how parts 1 a-d are related to the figure. 3. State the smallest value for so that you can view the complete graph of. 4. How many petals does have?

4. Repeat same steps for equation:. 1. 2. 3. 4.

5. Example 1 Analyze the graph of. Domain: Range: Continuity: Symmetry: Max r-value:

6. Summary: Rose Curves Forms: or ; (integer) Domain: all reals. Range: Continuous Symmetry: n(even), symmetry about x, y-axes and origin. n(odd),, symmetry about x-axis. n(odd),, symmetry about y-axis. Max r value: Number of petals: n if n is odd. 2n if n is even.

8. Example 2 Graph:

9. Example 3 Graph:

10. The graph of the equation is a circle that is symmetric w.r.t. the x- axis. Diameter from (0,0) to (a, 0) The graph of is a circle that is symmetric w.r.t. the y-axis. Diameter from (0, 0) to (a, ) Example 4 Graph: a. b.

11. Classwork Pg 683 #13,14,25-28.