If sin\( \theta \) = K find tan\(\theta\), 0^\circ \(\leq\) \(\theta\) \(\leq\) 90^\circ.
A
1-K
B
\( \frac{k}{k - 1} \)
C
\( \frac{k}{\sqrt{1 - k^2}} \)
D
\( \frac{k}{1 - k} \)
E
\( \frac{k}{\sqrt{ k^2 - 1}} \)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\sin \theta = \frac{k}{1}\)
\(\implies 1^2 = k^2 + adj^2\)
\(adj = \sqrt{1 - k^2}\)
\(\therefore \tan \theta = \frac{k}{\sqrt{1 - k^2}}\)
Source: Myschool Past Questions Archive (Record #22006)