Which of the following trigonometric functions is odd and has fundamental period \(2\pi\)?
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Answer and explanation
Correct answer: \(\sin x\)
Since \(\sin(-x)=-\sin x\), \(\sin x\) is an odd function, and its fundamental period is \(2\pi\). Although \(\tan x\) is also odd, its fundamental period is \(\pi\). In exams, verify each condition separately.
Frequently asked questions
What is the correct answer to this question?
\(\sin x\)
Why is this the correct answer?
Since \(\sin(-x)=-\sin x\), \(\sin x\) is an odd function, and its fundamental period is \(2\pi\). Although \(\tan x\) is also odd, its fundamental period is \(\pi\). In exams, verify each condition separately.
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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