# Tangent.What is the domain and range of y=-tan x?

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### 2 Answers

For the function y = -tan x, the function takes an undefined value at x = pi/2 + n*pi where cos x = 0. For all other x the function is defined.

This makes the domain of the function as all numbers except pi/2 + n*pi , where n is any integer.

The range is {R} as tan x can take on any real value.

Since the tangent function is an odd function, we'll re-write the given function as:

-tan x = tan (-x)

the domain of tangent function is (-pi/2 ; pi/2) or all real numbers, except pi/2 + kpi, k belongs to Z set of numbers.

For x = pi/2 + kpi, the tangent function is undefined.

Let's see why:

The tangent function is a ratio, where numerator is sine function and denominator is represented by cosine function:

tan x = sin x/cos x

If the denominator is zero, then the ratio is undefined. Since the cosine function is cancelling for x = pi/2 + kpi, then the ratio, namely tangent function, is undefined.

The range of tangent function is formed from all real numbers.

f(x) : (-pi/2 ; pi/2) -> R

f(x) = tan x