Consider the function \(f(\theta)=\operatorname{cosec}\left(\frac{\pi}{2}-\theta\right)\) for \(0 \leqslant \theta \leqslant 2 \pi\).
- Sketch the graph of \(y=\operatorname{cosec}\left(\frac{\pi}{2}-\theta\right)\), showing all key features. (2 marks)
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- In set notation, state the range of \(\theta\). (1 mark)
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Show Answers Only
a.
b. \(\text{Range} \ \ f(\theta):\ y \in(-\infty,-1] \cup[1, \infty)\)
Show Worked Solution
a. \(y=\operatorname{cosec}\left(\frac{\pi}{2}-\theta\right)=\dfrac{1}{\sin \left(\frac{\pi}{2}-\theta\right)}=\dfrac{1}{\cos\, \theta}\)
b. \(\text{Range} \ \ f(\theta):\ y \in(-\infty,-1] \cup[1, \infty)\)