Trigonometry For Dummies
Book image
Explore Book Buy On Amazon

The tangent and cotangent are related not only by the fact that they’re reciprocals, but also by the behavior of their ranges. In reference to the coordinate plane, tangent is y/x, and cotangent is x/y. The domains of both functions are restricted, because sometimes their ratios could have zeros in the denominator, but their ranges are infinite.

Domains of tangent and cotangent

Because x can’t equal 0 for the tangent function to work, this rule holds true: If

image0.png

or any odd multiple of 90 degrees. In radians,

image1.jpg

or any odd multiple of

image2.jpg

Both the tangent and secant functions have ratios with x in the denominator, making their domains the same.

In order for the cotangent function to work, y can’t equal 0. If

image3.png

or any multiple of 180 degrees. In radians,

image4.png

or any multiple of π.

Ranges of tangent and cotangent

The ranges of both tangent and cotangent are infinite, which, when expressed in mathematical notation, looks like this:

image5.png

The range values for these functions get very small (toward negative infinity) or very large (toward positive infinity) whenever the denominator of the respective ratio gets close to 0. When you divide some number by a very small value, such as 0.0001, the result is large. The smaller the denominator, the larger the result.

About This Article

This article is from the book:

About the book author:

Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others.

This article can be found in the category: