TITLE: Why $x^0=\frac{\pi x}{180}c$?
QUESTION [9 upvotes]: Differentiate $y=x^0\tan x^0$.

That's the main question. I simply know that anything to the power $0$ is equal to $1.$ But look what my book did.
$$y=\frac{\pi x}{180}\tan {\frac{\pi x}{180}}.$$
And, wrote as a side note $$x^0=\frac{\pi x}{180}c.$$
Is there any rule of it? It is little bit weird. I was learning $x^0=1.$ But here I am seeing something else.
Reason why I thought it was power instead of degree :

REPLY [2 votes]: The $ ^o$ means it is in degrees, not $0$. I know it looks confusing. Note that it multiplies by $\frac{\pi}{180}$, which is the conversion factor between degrees and radians. Now see if you can solve the problem knowing this fact.