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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.