Trigonometry Workbook For Dummies
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In trigonometry, tangent values go from negative infinity to positive infinity. So when you multiply the entire tangent function by a number, here’s what happens: If you multiply by a number bigger than 1, the function gets steeper more quickly; if you multiply by a fraction between 0 and 1, it gets flatter. And if you multiply by a negative number, the curve flips over the x-axis. (A flip is also called reflection.)

The graphs of the tangent function and two multiples.
The graphs of the tangent function and two multiples.

The preceding figure shows graphs of the basic tangent function (y = tan x) and two multiples to illustrate this property.

Notice in the figure how the multiplier of 6 makes the tangent curve steeper, whereas the multiple of 0.2 makes it flatten out. Both functions still have values that go from negative infinity to positive infinity, but the rate at which they get there changes.

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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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