Trigonometry Workbook For Dummies
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In trigonometry, multiplying the angle variable in a tangent function has the same effect as it does with sine and cosine functions — it affects the period of the function. If the multiple is 2, as in y = tan 2x, then the tangent function makes twice as many cycles in the usual amount of space. In other words, the period is p/2, which is the tangent’s usual period, p, divided by 2.

The graph of the tangent function and two multiples of the angle variable.
The graph of the tangent function and two multiples of the angle variable.

The preceding figure shows a few graphs to illustrate the effect of multiplying the angle variable by a number greater than 1 and then by a number between 0 and 1.

The graph of y = tan 3x doesn’t show all the asymptotes, but that graph has three times as many tangent curves as usual. The graph of

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only half as many cycles — or it takes twice as long to complete one cycle.

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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