Mathematics corresponding value of h in the function r(x)

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Mathematics corresponding value of h in the function r(x)

Step 1. Do the following adjustment with the sliders so that, a = 2, h = 2, b = 0, and c = 0 and then change the value of t from 0° to 360°. Answer the followings;
a) Which directions do A and C points move as t changes from 0° to 360°?
Answer (type in Blue):
GeoGebra Screenshot:

b) Now change value of a from 1 to 5. What do you see?
Answer (type in Blue):

GeoGebra Screenshot:

Step 2. Set a = 2. Then change the value of h from 1 to 2, to 3, … , to 10, copy the value of h below, and write the number of petals and the function r(x) for each value of h. (r(x) is in grey on the last line displayed in the left side bar).
h Number of petals r(x)

GeoGebra Screenshot: (copy and paste at least five screenshots for step-2)
GeoGebra Screenshot:
GeoGebra Screenshot:
GeoGebra Screenshot:
GeoGebra Screenshot:
GeoGebra Screenshot:

Answer the following questions;
a) What is the corresponding value of h in the function r(x)?
Answer:

b) Write function r(x) using coefficient a and h.
Answer:

c) What is the relationship between h and number of petals?
Answer:

d) Can we create a rose curve with 6 or 10 petals? Why or Why not?
Answer:

Step 3. Now set a = 1 and c = 1. As the value of h change from 1 to 5, copy the value of h, number of petals and the function r(x) on the left hand side bar.
h Number of petals or shape r(x)

GeoGebra Screenshot:(copy and paste at least five screenshots for step-3 depending on the values of h)
GeoGebra Screenshot:
GeoGebra Screenshot:
GeoGebra Screenshot:
GeoGebra Screenshot:
GeoGebra Screenshot:

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Now answer the following questions;
a) What is the corresponding value of h in the function r(x)? Write function r(x) using coefficient a, c and h.

b) What is the relationship between h and number of petals?

e) Make your guess about the function that generates 6 or 10 petals. Check your conjecture by changing the value of h. Is the relationship between h and the number of petals the same as in step 2. Copy the graph of the 6-petals rose.

Step 4: Set a = 0, c =0 and b = 2. Do step 2 and 3 replace a by b and h by k. Compare the graph when a=0, b = 1, c = 1 and k = 6 with the graph you copy on Step 3.
k Number of petals or shape r(x)
GeoGebra Screenshot: (copy and paste at least two screenshots)
GeoGebra Screenshot:
GeoGebra Screenshot:
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