Question

At which values of is the function y = sec theta undefined?

Answer 1

Given:

$\sec \theta=\infty$

To find the value of the angle:

It can be written as,

$\begin{gathered} \sec \theta=\infty \\ \frac{1}{\cos \theta}=\infty \\ \cos \theta=0 \\ \theta=\cos ^{-1}(0) \\ \theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2}\ldots\text{.} \end{gathered}$

Thus, the answer is,

$odd\text{ multiples of }\frac{\pi}{2}$

Hence, the correct option is D.