limit as x approaches infinity for $y=sec^{(-1)}x$

I'm a beginner and I'm using a basic graphing calculator. I understand I can input $sec^{(-1)}x$ as $cos^{(-1)}(1/x)$, but even as I'm looking at the graph, I don't get it. How do I determine the answer to be $\pi/2$? Thanks in advance for any help.

1 Answer

$$\sec^{-1}x=\cos^{-1}(1/x)$$ Take the limit: $$\lim_{x\to\infty}\sec^{-1}x=\lim_{x\to\infty}\cos^{-1}(1/x)\to\cos^{-1}(0)=\pi/2\mbox{ in the interval $[0,\pi]$.}$$