﻿ Draw the graph of cos2x in a period
back to Trigonometry video class

# Draw the graph of y = cos2x

The standard Cosine function is y = A cos (Bx + c). A is the amplitude, B is angular frequency and C is the phase shift. The given function is y = cos2x. In this case, A = 1, B = 2 and C = 0. The period T = 2pi/B = 2pi/2 = pi. So, the curve of y = cos2x will repeat in very pi interval. Now we use the five points to draw the y = cos2x curve in a period. Since a period is pi, then half period is pi/2, quarter period is pi/4, and three-quarter period is 3pi/4. So, x1 = 0, x2 = pi/4, x3 = pi/2, x4 = 3pi/4, x5 = pi. Now we need to find corresponding y value for each x value. When x1 = 0, y1 = cos (2 × 0) = cos0 = 1, so, the first point is (0, 1). When x = pi/4, y = cos (2 × pi/4) = cos(pi/2) = 0, so the second point is (pi/4, 0). When x = pi/2, y = cos (2 × pi/2) = cos(pi) = -1, so, he third point is (pi/2, -1). When x = 3pi/4, y = cos (2 × 3pi/4) = cos(3pi/2) = 0, so the fourth point is (3pi/4, 0). When x = pi, y = cos (2 × pi) = 1, so the fifth point is (pi, 1). Now we get these five points (0, 1), (pi/4, 0), (pi/2, -1), (3pi/4, 0), (pi, 1). Now connect the five points smoothly, we get the y = cos2x curve in a period. The curve of y = cos2x will repeat in every pi interval. The graph of y = cos2x will tend to positive x-axis and negative x-axis directions.