What is the range of the function \(f(x)=\cos x\) when \(x\in[0,\pi]\)?
Answer and explanation
Correct answer: \([-1,1]\)
On the interval \([0,\pi]\), \(\cos x\) decreases continuously from \(\cos 0=1\) to \(\cos\pi=-1\). Since both endpoints are included, every value from \(-1\) to \(1\) is attained, so the range is \([-1,1]\). Exam tip: for cosine over \([0,\pi]\), check the endpoint values first; they give the complete range.
Frequently asked questions
What is the correct answer to this question?
\([-1,1]\)
Why is this the correct answer?
On the interval \([0,\pi]\), \(\cos x\) decreases continuously from \(\cos 0=1\) to \(\cos\pi=-1\). Since both endpoints are included, every value from \(-1\) to \(1\) is attained, so the range is \([-1,1]\). Exam tip: for cosine over \([0,\pi]\), check the endpoint values first; they give the complete range.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Domain, range, and graphs of trigonometric functions.
