What is \(\cos(\theta+2\pi)\) equal to?
Answer and explanation
Correct answer: \(\cos \theta\)
The cosine function has period \(2\pi\). Therefore, adding \(2\pi\) returns the point to the same position on the unit circle, giving \(\cos(\theta+2\pi)=\cos\theta\). In contrast, adding \(\pi\) gives \(\cos(\theta+\pi)=-\cos\theta\). Exam tip: for both sine and cosine, adding \(2\pi\) leaves the value unchanged.
Frequently asked questions
What is the correct answer to this question?
\(\cos \theta\)
Why is this the correct answer?
The cosine function has period \(2\pi\). Therefore, adding \(2\pi\) returns the point to the same position on the unit circle, giving \(\cos(\theta+2\pi)=\cos\theta\). In contrast, adding \(\pi\) gives \(\cos(\theta+\pi)=-\cos\theta\). Exam tip: for both sine and cosine, adding \(2\pi\) leaves the value unchanged.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
