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Given that \(\theta\) is an acute angle and sin \(\theta\) = \(\frac{m}{n}\), find cos \(\theta\)

Mathematics
JAMB 1992

Given that \(\theta\) is an acute angle and sin \(\theta\) = \(\frac{m}{n}\), find cos \(\theta\)

  • A. \(\frac{\sqrt{n^2 - m^2}}{m}\)
  • B. \(\frac{\sqrt{(n + m)(n - m)}}{n}\)
  • C. \(\frac{m}{\sqrt{n^2 - m^2}}\)
  • D. \(\sqrt{\frac{n}{n^2 - m^2}}\)
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Correct Answer: Option B
Explanation

sin \(\theta\) = \(\frac{m}{n}\) 

Opp = m; Hyp = n

Adj = \(\sqrt{n^{2} - m^{2}}\)

\(\cos \theta = \frac{\sqrt{n^{2} - m^{2}}}{n}\)

= \(\frac{\sqrt{(n + m)(n - m)}}{n}\)


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