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Trigonometric ratios of related, double and half angles in terms of a given cosine

Trigonometric ratios of related, double and half angles in terms of a given cosine

IB Year 6 | Grade 12
6 marks

Given that \(\cos70^\circ=t\), find, in terms of \(t\), an expression for each of the following.

  1. \(\sin70^\circ\)[1]
  2. \(\cos140^\circ\)[1]
  3. \(\sin35^\circ\)[1]
  4. \(\sin160^\circ\)[1]
  5. \(\tan110^\circ\)[1]
  6. \(\cos250^\circ\)[1]

Solution:

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Answer:(a) \(\sqrt{1-t^2}\) (b) \(2t^2-1\) (c) \(\sqrt{\dfrac{1-t}{2}}\) (d) \(t\) (e) \(-\dfrac{\sqrt{1-t^2}}{t}\) (f) \(-t\)

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