What is \(\sin(2\pi+x)\) equal to?
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Answer and explanation
Correct answer: \(\sin x\)
The sine function has period \(2\pi\). Hence, adding \(2\pi\) to any angle \(x\) does not change its sine: \(\sin(2\pi+x)=\sin x\). The value \(-\sin x\) occurs on adding \(\pi\), since \(\sin(\pi+x)=-\sin x\). Exam tip: remember \(\sin(x+2n\pi)=\sin x\).
Frequently asked questions
What is the correct answer to this question?
\(\sin x\)
Why is this the correct answer?
The sine function has period \(2\pi\). Hence, adding \(2\pi\) to any angle \(x\) does not change its sine: \(\sin(2\pi+x)=\sin x\). The value \(-\sin x\) occurs on adding \(\pi\), since \(\sin(\pi+x)=-\sin x\). Exam tip: remember \(\sin(x+2n\pi)=\sin x\).
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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