What is \(\cos(2\pi+x)\) equal to?
Answer and explanation
Correct answer: \(\cos x\)
The cosine function has period \(2\pi\). Therefore, adding \(2\pi\) to any angle \(x\) does not change its cosine: \(\cos(x+2\pi)=\cos x\). Hence, \(\cos x\) is correct. The expression \(-\cos x\) occurs on adding \(\pi\), since \(\cos(x+\pi)=-\cos x\). Exam tip: Remember that both \(\sin x\) and \(\cos x\) have period \(2\pi\).
Frequently asked questions
What is the correct answer to this question?
\(\cos x\)
Why is this the correct answer?
The cosine function has period \(2\pi\). Therefore, adding \(2\pi\) to any angle \(x\) does not change its cosine: \(\cos(x+2\pi)=\cos x\). Hence, \(\cos x\) is correct. The expression \(-\cos x\) occurs on adding \(\pi\), since \(\cos(x+\pi)=-\cos x\). Exam tip: Remember that both \(\sin x\) and \(\cos x\) have period \(2\pi\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
