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How to draw the graph of y = sin(x - pi)
- Method 1: using phase shift
- Step 1: draw the graph of y = sin(x)

- Step 2: move the graph of y = sin(x) right pi units (pi = 3.14) to get the graph of y = sin(x - pi)

- Method 2: using formula
- y = sin(x - pi)
- = sin[-(pi - x)]
- = - sin(pi - x)
- = - sin(x)
- formula used:
- (1). sin(-x) = - sin(x)
- (2). sin(pi - x) = sin(x)
- Step 1: Draw the y = sin(x) curve

- Step 2: multiply -1 to the y = sin(x) graph to get the graph of y = sin(x - pi)

- Check
- when x = 0, y = sin(x - pi) = sin(0 - pi) = sin(-pi) = - sin(pi) = 0
- when x = pi/2, y = sin(x - pi) = sin(pi/2 - pi) = sin(pi/2 - 2pi/2) = sin(-pi/2) = -sin(pi/2) = -1
- when x = pi, y = sin(x - pi) = sin(pi - pi) = sin(0) = 0
- when x = 3pi/2, y = sin(x - pi) = sin(3pi/2 - pi) = sin(3pi/2 - 2pi/2) = sin(pi/2) = 1
- when x = 2pi, y = sin(x - pi) = sin(2pi - pi) = sin(pi) = 0
- Therefore, the five points of the graph y = sin(x - pi) are:
- (0, 0); (pi/2, -1); (pi, 0); (3pi/2, 1); (2pi, 0)
- pi = 3.14, the five points of graph y = sin(x - pi) are:
- (0, 0); (1.57, -1); (3.14, 0); (4.71, 1); (6.28, 0)
- The graph of y = sin(x - pi) repeat at the period of 2pi.