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).