Trigonometry - Exact Trigonometric Values and the Unit Circle

Trigonometry - Exact Trigonometric Values and the Unit Circle

Given that \(\cot \theta = 8\) and \(\theta\) is acute, without using a calculator, find,

  1. \(\sec \left( \frac{\pi}{2} - \theta \right)\),
  2. \(\cot \left( \frac{\pi}{2} - \theta \right)\),
  3. \(\textbf{cosec} \left( \frac{\pi}{2} - \theta \right)\),

exactly.

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Answer:(i) \(\sqrt{65}\) (ii) \(\frac{1}{8}\) (iii) \(\frac{\sqrt{65}}{8}\)

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