Finding the slope of a parametric equation

**iflyboats** · May 19th 2011, 11:20 AM

You're given the parametric equation of a curve:

$ x(t) = t^b\cos(2\pit) y(t) = t^b/sin(2\pit) $

Find the slope of the graph when t > 0.

$ x'(t) = (t^b)(-\sin(2\pit))(2\pi) + (cos(2\pit))(bt^(b-1)) y'(t) = (t^b)(2\picos(2\pit)) + (sin(s\pit))(bt^(b-1)) $

Can anyone direct me to the thread that teaches you how to use LATEX??

**Ackbeet** · May 19th 2011, 11:41 AM

I have moved this thread into the forum which has all the help you need. Tip: use [tex][/tex] tags for now, instead of the math tags.

**Opalg** · May 19th 2011, 12:37 PM

Originally Posted by iflyboats

You're given the parametric equation of a curve:

$x(t) = t^b\cos(2\pi t)$
$y(t) = t^b\sin(2\pi t)$

Find the slope of the graph when t > 0.

$x'(t) = (t^b)(-\sin(2\pi t))(2\pi) + (\cos(2\pi t))(bt^{b-1})$
$y'(t) = (t^b)(2\pi\cos(2\pi t)) + (\sin(2\pi t))(bt^{b-1})$

Can anyone direct me to the thread that teaches you how to use LATEX??

Apart from replacing the [tex] [/tex] tags by [TEX] [/TEX], you need to be careful about a couple of other things:

1. Don't write \pit (TeX will think that "pit" is a command). Instead, you should leave a space after \pi. In fact, that is good practice with all TeX commands.

2. Use braces { }, not parentheses ( ), in expressions like t^{b-1}. Tex will only treat the first character after ^ as a superscript unless you use braces. If you write t^(b-1), it will come out as
$t^(b-1)$ ,
with just the opening parenthesis superscripted.

Finally, the dialect of TeX used in this forum is a bit touchy about carriage returns (basically, it doesn't like them). So write your equations as

[TEX] x = y [/TEX] (all on one line)

rather than

[TEX]
x=y
[/TEX],

and enclose each line of TeX in separate [TEX] [/TEX] tags.

Put those little things right, and your TeX will come out nicely, as above.

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