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# Draw the graph of cos 2x

The graph of y = A cos Bx has the property
(1). amplitude = |A|
(2). period = 2pi/B
For y = cos 2x
A = 1, B = 2
(1). amplitude = |A| = 1
(2). period = 2pi/B = 2pi/2 = pi
divide five points between x = 0 to x = pi
The five points are: x = 0, x = pi/4, x = pi/2, x = 3pi/4, x = pi
Now find the corresponding values of y = cos2x
Five points of y = cos 2x in one period
when x = 0, y = cos(2 × 0) = cos 0 = 1, the point is (0, 1)
when x = pi/4, y = cos(2 × pi/4) = cos(pi/2) = 0, the point is (pi/4, 0)
when x = pi/2, y = cos(2 × pi/2) = cos(pi) = -1, the point is (pi/2, -1)
when x = 3pi/4, y = cos(2 × 3pi/4) = cos(3pi/2) = 0, the point is (3pi/4, 0)
when x = pi, y = cos(2 × pi) = 1, the point is (pi, 1)
The five points are: (0, 1), (pi/4, 0), (pi/2, -1), (3pi/4, 0), (pi, 1)
The graph is: compare the graph of y = cos2x to y = cos(x) both y = cos2x and y = cos(x) have the same amplitude
the period of y = cos2x is pi and the period of y = cos(x) is 2pi
For y = cos(x), B = 1, its period is 2pi (pi = 3.14, 2pi = 6.28)
For y = cos2x, B = 2, its period is pi, the curve repeat 2 times from [0, 2pi]