JAMB - Mathematics (1992 - No. 30)
Given that \(\theta\) is an acute angle and sin \(\theta\) = \(\frac{m}{n}\), find cos \(\theta\)
\(\frac{\sqrt{n^2 - m^2}}{m}\)
\(\frac{\sqrt{(n + m)(n - m)}}{n}\)
\(\frac{m}{\sqrt{n^2 - m^2}}\)
\(\sqrt{\frac{n}{n^2 - m^2}}\)
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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