Trigonometry - Trigonometric Equations

Trigonometry - Trigonometric Equations

TGM Original Questions

Solve each of the following equations.

  1. \(\cos 2x \sin \left( x - \frac{\pi}{3} \right) = 0\), \(-\pi \leq x \leq \pi\)
  2. \(2 \sin^2 x - 3 \sin x - 5 = 0\), \(0 \leq x \leq 2\pi\)

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Answer:(i) \(x = -\dfrac{3\pi}{4}, -\dfrac{2\pi}{3}, -\dfrac{\pi}{4}, \dfrac{\pi}{4}, \dfrac{\pi}{3}, \dfrac{3\pi}{4}\); (ii) \(x = \dfrac{3\pi}{2}\)

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