Step-by-Step Graphing of a Sinusoid of the Form y = A sin(B(x - C)) + D  Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

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?

 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 = 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).

 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Donna Roberts