Question

Explain the key features of the graph of the cosine function

Answer 1

The cosine function . . .

-- Starts at '1' when the angle is zero, and
proceeds downward from there.

-- From there, it is a smooth curve that wiggles
up and down as the angle increases.

-- The function wiggles up and down between
the limits of +1 and -1.

-- It crosses the x-axis every time the angle increases
by 180° (π radians).

Answer 2

The trigonometric functions have features that are worthy of note. Among these features are the period and the amplitude. The graph of f(x)=cos x repeats itself along the x-axis by a certain distance. This distance is called the period. For the cosine function, the period is 2pi radians. It can also be observed that the graph goes up and down by a certain distance. This distance is called the amplitude. For the curve of f(x)=cos x, the amplitude is 1. The main difference between a cosine function and a sine function is that the former is symmetric with respect to the y-axis while the latter is symmetric with respect to the origin.