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Exact ratios from cotangent in the third quadrant

Exact ratios from cotangent in the third quadrant

IB Year 6 | Grade 12

Given that \(\cot x=\dfrac{8}{15}\) and \(180{}^\circ<x<270{}^\circ\), find the exact value of each of the following.

  1. \(\sin x\)
  2. \(\sec x\)
  3. \(\tan(-x)\)
  4. \(\sin(90{}^\circ-x)\)

Solution:

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Answer:(a) \(-\frac{15}{17}\) (b) \(-\frac{17}{8}\) (c) \(-\frac{15}{8}\) (d) \(-\frac{8}{17}\)

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