
Sinusoid: y = Asin(B(x  C)) + D
Of course, any graphing utility can produce an accurate graph of a sinusoid. But how do you accomplish this task if you must graph by hand? 

How to use your graphing calculator for graphing trig functions.
click here. 


Build a Sinusoidal Graph by hand:
y = Asin(B(x  C)) + D
Graph: y = 2sin(π(x  2))  5 
Step 
Directions 
Graph 
1. 
Draw the center line of the graph by graphing the horizontal line, y = D. 

2. 
Using the amplitude, A, draw two horizontal lines, y = D + A and
y = D  A, that will encase the sinusoidal graph. The sinusoid's maxima (plural of maximum) will lie on y = D + A and its minima will lie on y = D  A. 

3. 
Determine the period of the curve using B. Period = 2π / B. Once we start to draw the graph, a complete cycle of the function will be completed within 2 units, for this example.
The horizontal distance between maxima and minima is ½ the period. 

4. 
Plot the point (C, D) which will lie on the center line. This point will be half way between a maximum point and a minimum point. 

5. 
Locate a maximum and minimum which are horizontally 1/4 of the period before and after the point (C, D). Since (2,5) corresponds to (0,0) of the standard sine graph, y = sin x, the maximum point will be to the right of the point (2,5).
y = 2sin(π(x  2))  5


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