Question

Describe each of the following properties of the graph of the Cosine Function, f(theta) = cos(theta) and relate the property to the unit circle definition of cosine.

Amplitude
Period
Domain
Range
x-intercepts

I know how to find each of them, and what they are, but I don't know exactly how they relate to the unit circle.

Answer 1

well cos(theta)=x on the unit circle

Answer 2

the unit circle has the equation x^2+y^2=1

Answer 3

x is an element of [-1,1]
y is an element of [-1,1]

Answer 4

You get all possible outputs in the first rotation of the circle (that is from theta=0 to theta=2pi)

Answer 5

You can find the x-intercepts of the equation x^2+y^2=1 by setting y=0.
Whatever you find for x you can look the corresponding theta on the unit circle.