## How does the value of an inverse cosine function change when the unit of its argument changes?

How does the value of $\cos^{-1} \left ( 0.1 \, \textrm{cm} \right )$ differ from $\cos^{-1} \left ( 0.1 \, \textrm{m} \right )$?

This is an interesting question, especially because the question of units in trigonometric and inverse trigonometric functions is rarely discussed in mathematics textbooks.

If you’re interested, think this problem through on your own. Then check Problem of the Day 86 at my other site, on or after 23 April 2013, for a discussion.