Choice #1: 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

Amplitude = 1:
The Amplitude is the maximum distance from 0 the function can be. In the case of  that maximum distance is 1, because the unit circle has a radius of 1 and is centered at the origin, so the x value of a point on the circle can't be greater than 1.

Period = 
The period is the distance required for the function to complete one cycle. It takes  radians to make a full round of the unit circle, and after that  repeats, so it is the period.

Domain = 
When the function is given an angle it radians, it goes that distance around the unit circle, and then gives the x value of the point on the circle at that distance. There is no that would cause this function to be undefined, so it's domains is .

Range = 
The unit circle has a radius of 1 and is located at the origin so the x value of any point on the unit circle has to be between -1 and 1.

X-Intercepts: 
X-intercepts occur where a function evaluates to 0. For  this occurs at odd multiples of , as these are locations on the unit circle where the x value of the corresponding point on the circle is 0.