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Draw the graph of y = cos x sin x

Because sin(2x) = 2sin(x)cos(x), so sin(x)cos(x) = (1/2) sin(2x). Note: cos(x)sin(x) = sin(x)cos(x)

So, we need to draw the graph of y = sin(2x). Note: the graph of y = sin(2x) can be transfer from the graph of y = sin(x)

Step 1: Draw the graph of y = sin(x). The period of y = sin(x) is pi. We use the five points method. The first point is (0, 0), the second point is (pi/2, 1), the third point is (pi, 0), the fourth point is (3pi/2, -1) and the fifth point is (2pi, 0). Connect these five points smoothly to get the graph of y = sin(x) in one period. Extended the graph in both direction for every 2pi interval to get the graph of y = sin(x).

Step 2: Draw the graph of y = sin(2x). The standard sine function is y = A sin (Bx + C), its period is T = 2pi/B. So, the period of y = sin(2x) is pi. In graph of y = sin(x), for each point, keep the y-coordinate, shrink the x-coordinate to half. The first point is (0, 0), the second point is (pi/4, 1), the third point is (pi/2, 0), the fourth point is (3pi/4, -1), the fifth point is (pi, 0). Connect these five points smoothly to get the graph of y = sin(2x). Extended the graph in both direction for every pi interval to get the graph of y = sin(2x).

Step 3: For each point in y = sin(2x), keep the x-coordinate and shrink the y-coordinate to half. The first point is (0, 0), the second point is (pi/4, 1/2), the third point is (pi/2, 0), the fourth point is (3pi/4, -1/2), the fifth point is (pi, 0). Connect these five points smoothly to get the graph of y = (1/2)sin (2x). Extended the graph in both direction for every pi interval to get the graph of y = (1/2) sin(2x). The graph of y = (1/2) sin(2x) is the graph of y = cos(x)sin(x).