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Conversion to trigonometric form

Conversion to trigonometric form

IB Year 6 | Grade 12

Express the following in trigonometric and exponential forms.

  1. \(2\mathrm{cis}\left(\frac{\pi}{12}\right)\mathrm{cis}\left(\frac{\pi}{6}\right)\)
  2. \(\frac{\sqrt{32}\mathrm{cis}\left(\frac{\pi}{8}\right)}{\sqrt{2}\mathrm{cis}\left(-\frac{7\pi}{8}\right)}\)
  3. \(\left[\sqrt{2}\mathrm{cis}\left(\frac{\pi}{2}\right)\right]^4\)

Solution:

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Answer:(a) \(2\operatorname{cis}\frac\pi4,\ 2e^{i\frac\pi4}\) (b) \(4\operatorname{cis}\pi,\ 4e^{i\pi}\) (c) \(4\operatorname{cis}0,\ 4e^0\).

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