Question

Find the domains of tangent and cotangent functions​

Answer 1

Step-by-step explanation:

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.

Answer 2

QuestioN:-

Find the domains of tangent and cotangent functions.

AnsweR:-

The domain of the function y=tan(x) ) is all real numbers except the values where cos(x) is equal to 0 , that is, the values π2+πn for all integers n . The range of the tangent function is all real numbers.