# 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]