Which of the following statements about the function \(\tan x\) is correct?
Answer and explanation
Correct answer: It is undefined at \(x=\frac{\pi}{2}+n\pi\), where \(n\in\mathbb Z\).
Since \(\tan x=\frac{\sin x}{\cos x}\), it is undefined wherever \(\cos x=0\), i.e., at \(x=\frac{\pi}{2}+n\pi\). Its range is all real numbers, not \([-1,1]\). Exam tip: for a quotient trig function, first check where its denominator becomes zero.
Frequently asked questions
What is the correct answer to this question?
It is undefined at \(x=\frac{\pi}{2}+n\pi\), where \(n\in\mathbb Z\).
Why is this the correct answer?
Since \(\tan x=\frac{\sin x}{\cos x}\), it is undefined wherever \(\cos x=0\), i.e., at \(x=\frac{\pi}{2}+n\pi\). Its range is all real numbers, not \([-1,1]\). Exam tip: for a quotient trig function, first check where its denominator becomes zero.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
