Draw the graph of y = sin(2x - pi/3)

Question: Graw the graph of the function y = sin(2x - pi/3)

Solution:

Step1: draw the graph of y = sin(2x)

Compare the standard form of the sine function, y = A sin(Bx + c)

For, y = sin(2x), A = 1, B = 2, and C = 0

The period (T) of y = sin(2x) is T = 2pi/B = 2pi/2 = pi

so, the amplitude of y = sin(2x) is 1 and period is pi.

Use the five points method to draw the graph of y = sin(2x)

If x = 0, y = sin(2x) = sin(0) = 0

If x = pi/4, y = sin(2x) = sin(2 × pi/4) = sin(pi/2) = 1

If x = pi/2, y = sin(2x) = sin(2 × pi/2) = sin(pi) = 0

If x = 3pi/4, y = sin(2x) = sin(2 × 3pi/4) = sin(3pi/2) = -1

If x = pi, y = sin(2x) = sin(2pi) = 0

	x	0	pi/4	pi/2	3pi/4	pi
	y	0	1	0	-1	0

Step2: shift the graph of y = sin(2x) right pi/6 units to get the graph of y = sin(2x - pi/3).