Step-by-Step Graphing of a Sinusoid of the Form
y = A sin(B(x - C)) +
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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
TI-83+/84+ graphing calculator for graphing trig functions.
Click calculator.

Step-by-Step Graphing of a Sinusoid
y = A sin(B(x - C)) +

Step Directions Example
1. Example:  

 Draw the center line of the graph by graphing the horizontal line, y =

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).