Given \(\operatorname{cosec}\,\alpha=-\dfrac{17}{8}\) and \(\pi<\alpha<\dfrac{3 \pi}{2}\), find the exact values of
- \(\sec \alpha\) (2 marks)
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- \(\tan \alpha\) (1 mark)
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Show Worked Solution
a. \(\operatorname{cosec} \alpha=-\dfrac{17}{8} \ \Rightarrow \ \sin \alpha=-\dfrac{8}{17}\)
\(\text{Graphically, given} \ \ \pi<\alpha<\dfrac{3 \pi}{2}:\)
\(x=\sqrt{17^2-8^2}=15\)
\(\sec \alpha=-\dfrac{17}{15}\)
b. \(\tan \alpha=\dfrac{8}{15}\)