What is the range of the function (\tan x)?
Answer and explanation
Correct answer: \(( -\infty,\infty )\)
\(\tan x=\dfrac{\sin x}{\cos x}\) is defined wherever \(\cos x\ne0\). On every interval where it is defined, \(\tan x\) takes every real value from \(-\infty\) to \(\infty\). Hence its range is \(( -\infty,\infty )\). The interval \([-1,1]\) is the range of \(\sin x\) and \(\cos x\), not of \(\tan x\). Exam tip: the ranges of \(\tan x\) and \(\cot x\) are all real numbers.
Frequently asked questions
What is the correct answer to this question?
\(( -\infty,\infty )\)
Why is this the correct answer?
\(\tan x=\dfrac{\sin x}{\cos x}\) is defined wherever \(\cos x\ne0\). On every interval where it is defined, \(\tan x\) takes every real value from \(-\infty\) to \(\infty\). Hence its range is \(( -\infty,\infty )\). The interval \([-1,1]\) is the range of \(\sin x\) and \(\cos x\), not of \(\tan x\). Exam tip: the ranges of \(\tan x\) and \(\cot x\) are all real numbers.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
