Sinusoid:
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? 

StepbyStep Graphing of a Sinusoid
y = A sin(B(x  C)) + D
Step  Directions  Example 
1.  Example: 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. .
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 1/2 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). 
