How to draw the graph of y = 2 sin (x/2 - pi/3) + 1?
Question: Draw the graph of y = 2 sin (x/2 - pi/3) + 1
Solution:
Step 1:
Draw the graph of y = 2 sin (x/2) in one period using five points method. Compare the standard Sine function y = A sin (Bx + C) with the given sine function, we get A = 2, B = 1/2 and C = 0.
The minimum period T = 2pi/B = 2pi ÷ 1/2 = 4pi. The five points are:
- When x = 0, y = 2 sin (x/2) = 2 sin 0 = 0
- when x = pi, y = 2 sin (x/2) = 2 sin (pi/2) = 2 × 1 = 2
- when x = 2pi, y = 2 sin (x/2) = 2 sin (2pi/2) = 2 sin pi = 2 × 0 = 0
- when x = 3pi, y = 2 sin (x/2) = 2 sin (3pi/2) = 2 × -1 = -2
- when x = 4pi, y = sin (x/2) = 2 sin (4pi/2) = sin 2pi = 2 × 0 = 0
- The five point are: (0, 0), (pi, 2), (2pi, 0), (3pi, -2), and (4pi, 0).
- That is,
|
point 1 |
point 2 |
point 3 |
point 4 |
point 5 |
x : |
0 |
pi |
2pi |
3pi |
4pi |
y : |
0 |
2 |
0 |
-2 |
0 |
Step 2:
Draw the graph of y = 2 sin (x/2 - pi/3) = 2 sin [(1/2) (x - 2pi/3)] by shift the graph of y = 2 sin x/2 toward right 2pi/3 units.
Step 3:
Draw the graph of y = 2 sin (x/2 - pi/3) + 1 by move the graph of y = 2 sin (x/2 - pi/3) upward one unit.