Re: notation help: f(x) = (sin x)^(1/3)

• To: mathgroup at smc.vnet.net
• Subject: [mg29988] Re: [mg29947] notation help: f(x) = (sin x)^(1/3)
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Fri, 20 Jul 2001 03:28:52 -0400 (EDT)
• References: <200107190757.DAA02259@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```First, you must use parenthesis, instead of brackets, to enclose Sin[x].
Second, you must take into account that there are three cube roots of
Sin[x], and one of them is real, which is the one you want to plot.
Ordinarily, Mathematica chooses the root with the least positive argument,
and sometimes this turns out to be complex, which then of course won't
appear in the plot. Fortunately, there is a nice Add-On package called
the on-line Help. This is what you must do:

In[1]:=
Needs["Miscellaneous`RealOnly`"]
In[2]:=
Plot[(Sin[x])^(1/3), {x, -10, 10}];

This is the sort of thing that makes beginners (and others, too) irate.
However, Mathematica is a logical and well-designed engine, and that is
where its enormous power lies. There are three cube roots to any real
number; which one to choose? And of course, complex roots have the same
rights as real roots, so that, given a rule to choose a root, what if it
turns out to be complex? If one wants to plot, then it is nice to have a
mechanism which will only return roots. But one has to know about it, alas.

Tomas Garza
Mexico City

----- Original Message -----
From: "Tim 9-23" <bendoftimeb at stny.rr.com>
To: mathgroup at smc.vnet.net
Subject: [mg29988] [mg29947] notation help: f(x) = (sin x)^(1/3)

> How do I plot this.  I must not be entering it correctly.  It's the
> plot of the cube root of the Sine function.
>
> Plot[[Sin[x]]^(1/3), {x, -10, 10}] isn't working.  Thanks.
>
> My email address is anti-spammed.  Remove the 2 B's after hitting email