1. Polar Graphs: Rose By: Sandy Foley and Dan Sigman 27 February 2014 Period B

2. Formula for a Rose Graph The formula for a Rose graph takes the form of: R=a sin (nT) where T is the angle R=a cos (nT) where T is the angle Altering the values of a, n, or T will have significant changes in the shape of the graph.

3. The Effect of a on the Rose Graph The value of a stretches or shrinks the tips of the petals of the rose. For example, if a is 8, each petal of the rose will extend eight spaces from the center of the graph. Also, a must not be equal to zero. Whether a is positive or negative will not make a difference in the shape of the graph.

4. The Effect of Sine and Cosine on the Rose Graph Using cosine in the formula for a rose graph will rotate the petals so they are bisected by the x-axis and y-axis. Using sine in the formula will rotate the petals so that they extend freely into the quadrants. In the picture to the right, green is the cosine graph and red is the sine graph.

5. The Value of n on the Rose Graph (odd) When n is an odd number, the graph will have n petals.

6. The Value of n on the Rose Graph (even) When n is an even number, the number of petals will be double the value of n, or 2n.

7. The Value of n on the Rose Graph (negative) When n is a negative value, the rose graph is reflected over the x axis. In other words, it is rotated 180 degrees.

8. Adding/Subtracting Values to the Rose Equation When adding or subtracting a number to the end of the equation, the radius of the graph will increase in length, making the petals longer and wider.

9. Adding Values to the Rose Equation When adding values to the equation inside the parentheses, the graph will rotate either clockwise or counterclockwise depending on the number being added or subtracted in the parentheses. Subtracting will rotate the graph clockwise, and adding will rotate the graph counterclockwise.

10. Interactive Game For Extra Help http://binarylabs.info/index_files/polar_graphs/rose.html

11. Sources http://sites.csn.edu/istewart/mathweb/math127/polar_equ/polar_equ.htm http://mathworld.wolfram.com/Rose.html file:///C:/Users/sfoley/Downloads/Rose_Curve_Teacher.pdf http://campuses.fortbendisd.com/campuses/documents/Teacher/2006/teacher_2006041 3_0948.pdf http://campuses.fortbendisd.com/campuses/documents/Teacher/2006/teacher_2006041 3_0948.pdf http://www2.hoover.k12.al.us/schools/hhs/faculty/kjohnson/Documents/Precal%20Chapt er%208/Polar%20Equations%20and%20Graphs%20Day%203.pdf http://www2.hoover.k12.al.us/schools/hhs/faculty/kjohnson/Documents/Precal%20Chapt er%208/Polar%20Equations%20and%20Graphs%20Day%203.pdf