Valerie Russell

Assignment 11

Polar Equations

when a > 0:

The circle increases as a increases above the x-axis. The circle increases as a increases to the right of the x-axis.

when a < 0:

The circle increases as a increases below the x-axis. The circle increases as a inreases to the left of the x-axis.

Whether sine or cosine a represents the the diameter of the circle.

Let's investigate the polar equation for different values of n:

 Petals on a Rose with Cosine When n is 1,the graph looks like a heart as in the first polar equation. When n is 2, the graph has 2 petals. When n is 4, the graph has 4 petals. As n increases, the number of petals on the rose increases.
 Petals on a Rose with Sine Notice that changing the function from Cosine to Sine only changes the rotation. The picture remains the same

 Values of a Notice that changing the coefficient of a expands the polar equation. A coefficient of 2 expands the petals to 2 and a coefficient of 3 expands the petals to 3 and so on... Can you guess what n is in each equation? Hint: Remember to count the number of petals in the rose.

 Values of b: Notice the Cosine and Sine functions are going in opposite directions. As b increases, the functions stretch horizontally and vertically.