What is the range of (\cosec x)?
Answer and explanation
Correct answer: \((-\infty,-1]\cup[1,\infty)\)
\(\cosec x=\frac{1}{\sin x}\). Since \(-1\leq\sin x\leq 1\), and \(\sin x\neq0\) wherever cosecant is defined, its reciprocal satisfies \(\cosec x\leq-1\) or \(\cosec x\geq1\). Hence, the range is \((-\infty,-1]\cup[1,\infty)\). The interval \([-1,1]\) is the range of \(\sin x\), not of \(\cosec x\). Exam tip: reciprocal trigonometric functions cannot take values between \(-1\) and \(1\).
Frequently asked questions
What is the correct answer to this question?
\((-\infty,-1]\cup[1,\infty)\)
Why is this the correct answer?
\(\cosec x=\frac{1}{\sin x}\). Since \(-1\leq\sin x\leq 1\), and \(\sin x\neq0\) wherever cosecant is defined, its reciprocal satisfies \(\cosec x\leq-1\) or \(\cosec x\geq1\). Hence, the range is \((-\infty,-1]\cup[1,\infty)\). The interval \([-1,1]\) is the range of \(\sin x\), not of \(\cosec x\). Exam tip: reciprocal trigonometric functions cannot take values between \(-1\) and \(1\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
