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

f (theta) = cos (theta)

The cosine function reaches a maximum of + 1 and a minimum of - 1. Therefore, its amplitude is 1. The period is at what theta value the function repeats itself. The period for cosine and sine function is 2 (pi). Domain means what values are allowed for theta. There is no restriction. Theta can be: - infinity < theta < infinity. Or in interval notation, the domain is: (-infinity, infinity) Range, like we mentioned before, the cosine function has a minimum of - 1 and a maximum of + 1. Range is: [-1, 1] x-intercepts is where the curve cuts/touches the x-axis. Cosine function crosses the x-axis at pi/2, 3pi/2, 5pi/2, on the positive side and - pi/2, - 3pi/2, - 5pi/2, on the negative side. Or in general: plus/minus n*pi + pi/2 where n = 0, 1, 2, 3.