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.

Answer 1

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, ...