Consider the function \(y=\operatorname{cosec}\,x\) for \(-\pi \leqslant x \leqslant \pi\).
- State the equations of all vertical asymptotes in the given domain. (1 mark)
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- Sketch the graph of \(y=\operatorname{cosec} x\), showing all key features. (2 marks)
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a. \(y=\operatorname{cosec}\,x=\dfrac{1}{\sin x}\)
\(\text{Asymptotes when \(\ \sin x=0 \ \) in given domain.}\)
\(\therefore \ \text{Asymptotes at} \ \ x=-\pi, 0, \pi\)
b.
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a. \(y=\operatorname{cosec}\,x=\dfrac{1}{\sin x}\)
\(\text{Asymptotes when \(\ \sin x=0 \ \) in given domain.}\)
\(\therefore \ \text{Asymptotes at} \ \ x=-\pi, 0, \pi\)
b.