Which of the following statements correctly represents the range of \(\sin x\) for all real values of \(x\)?
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Answer and explanation
Correct answer: \(-1 \leq \sin x \leq 1\)
The value of \(\sin x\) always lies from \(-1\) to \(1\), and both endpoints occur: \(\sin(\pi/2)=1\) and \(\sin(3\pi/2)=-1\). Hence the endpoints must be included. Exam tip: use inclusive inequality signs for the range of sine.
Frequently asked questions
What is the correct answer to this question?
\(-1 \leq \sin x \leq 1\)
Why is this the correct answer?
The value of \(\sin x\) always lies from \(-1\) to \(1\), and both endpoints occur: \(\sin(\pi/2)=1\) and \(\sin(3\pi/2)=-1\). Hence the endpoints must be included. Exam tip: use inclusive inequality signs for the range of sine.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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