The definitions for the set of points (x, y) on the unit circle are defined as functions o...

The definitions for the set of points (x, y) on the unit circle are defined as functions of t: x = cos(t) = f(t),and y = sin(t) = g(t). In Chapter 6 we will discuss that these points are said to be defined parametrically and the equations x = cos(t) and y = sin(t) are called parametric equations. Use a graphing utility with the following settings:

MODE radian

parametric (par, para, param)

WINDOW Tmin = 0 Tmax = 2π

T step =

Xmin = -3 Xmax = 3

Ymin = -2 Ymax = 2

Input x2cos(t) and y1 = sin(t), and graph these parametric equations.

a. Describe the graph. Is the graph what you would expect?

b. Trace the curve and describe what's happening.

c. Why are you only able to trace the curve once?

d. What do you think will happen if you change Tmax to 4π (≈12.56)? Test your thinking by again tracing the curve with Tmax as 4π.

e. Trace the curve again and stop at different points on the unit circle. Notice that each time you stop, the screen displays values. A graphing calculator will display three values below the graph, as indicated in the accompanying screen. In the context of the circular functions, what does each value represent?