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

Answer 1

i'v got Amplitude = radius of circle, r.
period = time rate at which function moves from 0 to 2π
Domain: {0, 2π}
Range: {-r, +r}
x-intercepts at theta = π/2 and theta = 3π/2

Answer 2

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, ...

Answer 3

you are absolutely the BEST thank you so much (:

Answer 4

Oh, you are so kind. And you are welcome. :)