# Math Help - LaTeX - Practice 7-15-10

1. ## LaTeX - Practice 7-15-10

Note: Please reply to this post with any helpful suggestions regarding LaTeX and/or to correct any mathematical error(s) I made.

de Moivre's Theorem --

$z = r(cos{\theta} + i sin{\theta})$

$z^2 = r\cdot{r}(cos(\theta + \theta) + i sin(\theta + \theta))$

$z^2 = r^2(cos 2{\theta} + i sin 2{\theta})$

$z^3 = r^3(cos 3{\theta} + i sin 3{\theta})$

$z^4 = r^4(cos 4{\theta} + i sin 4{\theta})$

$z^n = r^n(cos n{\theta} + i sin n{\theta})$

Question: What is the method for inserting spaces between items?

2. $z^n= r^n(\cos n\theta+ i \sin n\theta)$

Trig functions look better like this, double click to see my code.

Leave a space... you can use '~'

$\int f(x)~dx$

3. Originally Posted by DeanSchlarbaum
Question: What is the method for inserting spaces between items?
TeX has four types of spaces available in math mode. They are \, (thin space), \: (medium space), \; (thick space) and \! (thin negative space). In practice, there are not many occasions when you need to use these spacings. The spacing provided automatically by TeX is usually optimal. The only times when I use manual spacing are in integrals and in modular arithmetic.

Compare $\displaystyle \int f(x)dx$ and $\displaystyle \int \!\! f(x) \, dx$. Also $x \equiv 1\pmod{p}$ and $x \equiv 1 \!\! \pmod{p}$.

4. Hello, DeanSchlarbaum!

DeMoivre's Theorem --

$z = r(cos{\theta} + i sin{\theta})$

$z^2 = r\cdot{r}(cos(\theta + \theta) + i sin(\theta + \theta))$

$z^2 = r^2(cos 2{\theta} + i sin 2{\theta})$

$z^3 = r^3(cos 3{\theta} + i sin 3{\theta})$

Question: What is the method for inserting spaces between items?

Trig functions (and others) look "nicer" if you precede them with a blackslash.

. . Compare: . $\begin{array}{cc}
sin x & \sin x \\
cos x & \cos x \\
ln x ^& \ln x \\
arcsin x & \arcsin x
\end{array}$

There are different-sized spaces that can be used:

. . . . . *\,* . . . . . . . . . . . $*\,*$

. . . . . *\:* . . . . . . . . . . . $*\:*$

. . . . . *\;* . . . . . . . . . . . $*\;*$

. . . *\quad* . . . . . . . . . . $*\quad*$

. . . *\qquad* . . . . . . . . $*\qquad*$

\phantom{xxxxxxx} . . $*\phantom{xxxxxxx}*$