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
\(\sqrt{\frac{n}{n^2 - m^2}}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
sin \(\theta\) = \(\frac{m}{n}\)
Opp = m; Hyp = n
Adj = \(\sqrt{n^{2} - m^{2}}\)
\(\cos \theta = \frac{\sqrt{n^{2} - m^{2}}}{n}\)
= \(\frac{\sqrt{(n + m)(n - m)}}{n}\)
Source: Myschool Past Questions Archive (Record #31349)