Assignment 11

By: Olamide Alli

Exploration: Investigate the graphs of r = a +bcos(kӨ)

Let’s start with a =1, b =1, and k = 1

Let’s try changing the value of k, but keeping a and b constant.

From the graphs above we can deduce that k corresponds to n, where n represents the number of leaves on the n-leaf rose. Also notice that the x-intercepts of each graph is 2, and in some cases -2, which is the value of +/- (a+b).

If we let k= .5

You must double your rotations to get a complete graph. We can see there are 2 inverted leaves.

When k = .25

We must increase the # of rotations by 4 to get a complete graph. Notice that we now have 4 leaves inverted in each other.

Now let’s look at graphs of when the values of k and b are varied and a is the constant.

Now we have a double leaf rose. Notice k = n for small leaves as well as k = n for larger leaves.

Notice that the x intercepts are still equated to +/- (a+b), and as b increases the length of the second set of leaves elongates.

What if cos() is replaced with sin()?

The shape of the graph stays the same but when the translated from cosine to sine the graph is rotated 90°.