What is the range of the function (\sin x)?

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 \([-1,1]\).