The graph of a cosine function y = cos x is looks like this:
Range: [–1, 1] or
y -intercept: (0, 1)
x -intercept: , where n is an integer.
Continuity: continuous on
Symmetry: y -axis (even function)
The maximum value of y = cos x occurs when , where n is an integer.
The minimum value of y = cos x occurs when , where n is an integer.
The amplitude of the graph of y = a cos bx is the amount by which it varies above and below the x -axis.
Amplitude = | a |
The period of a cosine function is the length of the shortest interval on the x -axis over which the graph repeats.
Sketch the graphs of y = cos x and y = 2 cos x . Compare the graphs.
For the function y = 2 cos x , the graph has an amplitude 2. Since b = 1, the graph has a period of . Thus, it cycles once from 0 to with one maximum of 2, and one minimum of –2.
Observe the graphs of y = cos x and y = 2 cos x . Each has the same x -intercepts, but y = 2 cos x has an amplitude that is twice the amplitude of y = cos x .
Also see Trigonometric Functions.