Given \(\cot \theta=-\dfrac{12}{5}\) and \(\dfrac{\pi}{2}<\theta<\pi\), find the exact values of
- \(\sec \theta\) (2 marks)
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- \(\sin \theta\) (1 mark)
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Show Worked Solution
a. \(\cot \theta=-\dfrac{12}{7} \ \Rightarrow \ \tan \theta=-\dfrac{7}{12}\)
\(\text{Graphically, given} \ \ \dfrac{\pi}{2}<\theta<\pi:\)
\(x=\sqrt{7^2+12^2}=13\)
\(\sec \theta=-\dfrac{13}{12}\)
b. \(\sin \theta=\dfrac{7}{13}\)