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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.

Related tags

Trigonometric FunctionsTangent FunctionDomain Of TanUndefined ValuesClass 11 MathematicsTrigonometric Functions And Their PropertiesMathematicsClass 12 Mcq

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