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Trigonometry - Symmetry of Trigonometric Functions

Trigonometry - Symmetry of Trigonometric Functions

TGM Original Questions

Given that \(\sin \beta = -\frac{3}{4}\) and \(\cos \beta > 0\), find the value of each of the following without using a calculator.

  1. \(\cos \beta\)
  1. \(\sin(-\beta)\)
  1. \(\sec \beta\)
  1. \(\tan \beta\)
  1. \(\sin\left(\frac{\pi}{2} - \beta\right)\)
  1. \(\mathrm{cosec} \, \beta\)

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Answer:(i) \(\frac{\sqrt7}{4}\) (ii) \(-\frac{3\sqrt7}{7}\) (iii) \(\frac{3}{4}\) (iv) \(\frac{\sqrt7}{4}\) (v) \(\frac{4\sqrt7}{7}\) (vi) \(-\frac{4}{3}\)

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