Which of the following trigonometric functions is an even function, has least positive period \(\pi\), and has range \([-1,1]\)?
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Answer and explanation
Correct answer: \(\cos 2x\)
Since \(\cos(-2x)=\cos 2x\), \(\cos 2x\) is even. Replacing \(x\) by \(x+\pi\) leaves it unchanged, and its range is \([-1,1]\). Although \(\sec 2x\) is even, its range excludes values between \(-1\) and \(1\). Exam tip: test \(f(-x)\) for parity.
Frequently asked questions
What is the correct answer to this question?
\(\cos 2x\)
Why is this the correct answer?
Since \(\cos(-2x)=\cos 2x\), \(\cos 2x\) is even. Replacing \(x\) by \(x+\pi\) leaves it unchanged, and its range is \([-1,1]\). Although \(\sec 2x\) is even, its range excludes values between \(-1\) and \(1\). Exam tip: test \(f(-x)\) for parity.
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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