Which of the following trigonometric functions has domain \(x\ne \frac{(2n+1)\pi}{2}\), where \(n\in\mathbb{Z}\), and range \(( -\infty,-1]\cup[1,\infty)\)?
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Answer and explanation
Correct answer: \(\sec x\)
Since \(\sec x=1/\cos x\), it is undefined when \(\cos x=0\), i.e. at \(x=\frac{(2n+1)\pi}{2}\). Also, \(|\sec x|\ge1\), giving the stated range. For \(\csc x\), the excluded values are \(n\pi\). Exam tip: first locate angles that make the denominator zero in reciprocal functions.
Frequently asked questions
What is the correct answer to this question?
\(\sec x\)
Why is this the correct answer?
Since \(\sec x=1/\cos x\), it is undefined when \(\cos x=0\), i.e. at \(x=\frac{(2n+1)\pi}{2}\). Also, \(|\sec x|\ge1\), giving the stated range. For \(\csc x\), the excluded values are \(n\pi\). Exam tip: first locate angles that make the denominator zero in reciprocal functions.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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