What is the range of the function (\sin x)?
Answer and explanation
Correct answer: \([-1,1]\)
For real values of \(x\), \(\sin x\) always lies between \(-1\) and \(1\). It attains \(1\) at \(x=\frac{\pi}{2}\) and \(-1\) at \(x=\frac{3\pi}{2}\), so its range is \([-1,1]\). The interval \([0,1]\) includes only the non-negative sine values, so it is not the complete range. Exam tip: remember that both sine and cosine have range \([-1,1]\).
Frequently asked questions
What is the correct answer to this question?
\([-1,1]\)
Why is this the correct answer?
For real values of \(x\), \(\sin x\) always lies between \(-1\) and \(1\). It attains \(1\) at \(x=\frac{\pi}{2}\) and \(-1\) at \(x=\frac{3\pi}{2}\), so its range is \([-1,1]\). The interval \([0,1]\) includes only the non-negative sine values, so it is not the complete range. Exam tip: remember that both sine and cosine have range \([-1,1]\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
