Discussion
If \(3\sin\theta = 4\cos\theta\), then the value of \(\sec\theta\) is
Answer: B
The value of \(\sec\theta\) is \(\frac{5}{3}\).
From \(3\sin\theta = 4\cos\theta\), \(\tan\theta = \frac{4}{3}\). Take a right triangle with opposite side 4 and adjacent side 3; its hypotenuse is 5:
\[ \begin{aligned} \sec\theta &= \frac{\text{hypotenuse}}{\text{adjacent}} \\ &= \frac{5}{3} \end{aligned} \]
\(\frac{5}{4}\) is \(\csc\theta\), \(\frac{4}{3}\) is \(\tan\theta\) and \(\frac{3}{4}\) is \(\cot\theta\), the usual ways of mixing up the ratios.
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