Sinusoid:
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Of course, any graphing utility can produce an accurate graph of a sinusoid. But how to you accomplish this task if you must graph by hand? |
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Step-by-Step 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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). |
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