1. In the investigation you used the parametric equations for a circle, x = 3cos t and y = 3 sin t, to graph other geometric shapes on your calculator. Mathematically, do you think it is correct to say that x = 3 cos t and y = 3 sin t are the parametric equations of a square or a hexagon? Explain your reasoning.
2. Find parametric equations for each translated circle.
a.

b.

c.

d.

3. Use the parametric equations x = 3 cos t and y = 3 sin t to make each of these figures on your calculator. What range of t-values and what t-step are required for each?
a.

b.

c.

d.

4. Consider a unit circle (a circle with radius 1) centered at the origin.

a. What are the parametric equations for the unit circle?
b. From Chapter 4, you know that the Pythagorean Theorem yields the equation of the unit circle, x2 + y2 = 1. Substitute the parametric equations for x and y to get an equation in terms of sine and cosine.
c. Use your calculator to verify that your equation in 4b is true for t = 47°.
5. Experiment to find parametric equations for each ellipse.
a.

b.

c.

d.

Transcribed Image Text:

-47, 47, 1.-31.31, 1] (U, 0)r