Graph of $(\sin x)^x$

Question

How can you plot the graph for the function $(\sin x)^x$? My problem is that $\sin(x)$ can assume negative values too, so it is not like a standard exponential function. Any help would be appreciated.

Answer 1

Yep, the function (from $\mathbb{R}$ to $\mathbb{R}$) is not defined for all real numbers, so we need to make a restriction on the domain from all the reals to the sets $\ldots(-4\pi,-3\pi)$, $(-2\pi,-\pi)$, $(0, \pi)$, $(2\pi, 3\pi)$, $(4\pi, 5\pi)\ldots$ in order to have a well defined function. Hopefully this helps.

Answer 2

It's quite difficult to plot these points and making the guesses about it, however I am not saying it's impossible but it'll take you forever. So here I am providing you it's graph to make it easier.

$$(\sin x)^x$$

Answer 3

I think we can change the undefined points to be defined, for example, we can plot the graph for the function $|\sin x|^x$ first. Then because those values of $x$ which make $\sin x<0$ are not in the domain, we can erase them from the graph.