Amplitude = 1:
The Amplitude is the maximum distance from 0 the function can be. In the case of [tex]cos(\theta)[/tex] 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 = [tex]2\pi[/tex]
The period is the distance required for the function to complete one cycle. It takes [tex]2\pi[/tex] radians to make a full round of the unit circle, and after that [tex]cos(\theta)[/tex] repeats, so it is the period.
Domain = [tex]\mathbb{R}[/tex]
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 [tex]\theta[/tex] that would cause this function to be undefined, so it's domains is [tex]\mathbb{R}[/tex].
Range = [tex]\{\theta \: | \: -1 \leq \theta \leq 1 \}[/tex]
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: [tex]\frac{n\pi}{2} \:\: where\: n\: is \:any \:odd \:integer[/tex]
X-intercepts occur where a function evaluates to 0. For [tex]cos(\theta)[/tex] this occurs at odd multiples of [tex]\frac{\pi}{2}[/tex], as these are locations on the unit circle where the x value of the corresponding point on the circle is 0.
