What is \(\cos(2\pi+\theta)\) equal to?
Answer and explanation
Correct answer: \(\cos \theta\)
The cosine function has period \(2\pi\). Therefore, \(\cos(\theta+2\pi)=\cos\theta\), so \(\cos(2\pi+\theta)=\cos\theta\). The expression \(-\cos\theta\) results when \(\pi\) is added to the angle: \(\cos(\theta+\pi)=-\cos\theta\). Exam tip: Adding or subtracting any integral multiple of \(2\pi\) leaves the values of sine and cosine 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, \(\cos(\theta+2\pi)=\cos\theta\), so \(\cos(2\pi+\theta)=\cos\theta\). The expression \(-\cos\theta\) results when \(\pi\) is added to the angle: \(\cos(\theta+\pi)=-\cos\theta\). Exam tip: Adding or subtracting any integral multiple of \(2\pi\) leaves the values of sine and cosine 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.
