If cot \(\theta\) = \(\frac{x}{y}\), find cosec\(\theta\)

  • A \(\frac{1}{y}\)(x2 + y2)
  • B \(\frac{x}{y}\)
  • C \(\frac{1}{y}\)\(\sqrt{x^2 + y^2}\)
  • D \(\frac{x - y}{y}\)
jamb 1988mathematics

The correct answer is C. \(\frac{1}{y}\)\(\sqrt{x^2 + y^2}\)

\(\cot \theta = \frac{x}{y}\)

\(\implies \tan \theta = \frac{y}{x}\)

\(opp = y; adj = x\)

Using Pythagoras theorem, \(Hyp^{2} = Opp^{2} + Adj^{2}\)

\(Hyp^{2} = y^{2} + x^{2}\)

\(Hyp = \sqrt{y^{2} + x^{2}}\)

\(\sin \theta = \frac{y}{\sqrt{y^{2} + x^{2}}}\)

\(\therefore \csc \theta = \frac{\sqrt{y^{2} + x^{2}}}{y}\)

= \(\frac{1}{y}(\sqrt{y^{2} + x^{2}})\)

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