## LaTex guide

SATmath4u.com is the first forum introducing the addition of LaTeX mathematical typesetting for SAT math test.
LaTeX is a professional-grade general typesetting system that centers around very pleasing mathematical presentation. Mathematical expressions are written in a markup style somewhat similar to HTML.
You may include LaTeX graphics in any post here on SATmath4u.com
To include a LaTeX graphic, simply include your LaTeX code within the tags [tex][ /tex]. without spaces.
Or by using the rightmost button in editing bar and then use the math symbols bellow the post area as shown in the following image.

Basic Guidelines
Lines and Text. \\ starts a new line, \ includes a space, \mbox{...} includes text

Sub- and Superscripts.
Code:
 [tex]x^3[ /tex]
produces while
Code:
[tex]x_{2n}[  /tex]
produces
Here is another example:
Code:
[tex]\log_{5} 125=3[  /tex]
gives

Fractions. Use \frac to display fractions.
Example:
Code:
[tex]\frac{\pi^2}{6}[  /tex]
gives .

Roots. Use \sqrt. For instance,
Code:
[tex]\sqrt{a^3+b^4}[  /tex]
produces

You can also get “other” roots:
Code:
[tex]\sqrt[4]{5}[  /tex]
yields .

Various examples
Code:
Code:
[tex] \frac{1}{2^n} \rightarrow 0[  /tex]
produces the graphic

Code:
Code:
[tex]\int_a^b f(t) dt = 1[  /tex]
produces the graphic

Code:
Code:
[tex] \sum_{n=0}^{\infty} \frac{1}{n!} = e [  /tex]
produces the graphic

Plus or minus

Code:
[tex]\pm[  /tex]
produces the graphic

multiplication or dot product

Code:
[tex]a\cdot b[  /tex]
produces the graphic

Equals sign and inequalities

To get an equals sign, you simply use the ordinary = sign.
Code:
 [tex]2+3=5[  /tex]
produces the graphic

For 'not equal to', use \not=

Code:
[tex]2^4\not=2[  /tex]
produces the graphic

For less than signs, we use <, and for greater than signs, we use >

For 'less than or equal to' signs, we use \leq, and for 'greater than or equal to' signs we use \geq

Code:
[tex]x^2 \geq 0[  /tex]
produces the graphic

For spaces, use "\ ".

Sigma notation

To write sums, we use the \sum command.

Code:
[tex]\sum_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1) [  /tex]
produces the graphic

Differentiation

We use \frac{}{} to write dy/dx.

Code:
[tex]\frac{d}{dx} x^4 = 4x^3[  /tex]
produces the graphic

For f'(x), simply write it out normally within TeX tags.

Code:
[tex]f'(x)[  /tex]
produces the graphic

Integration

For the integral sign, use the \int command.

Code:
[tex]\int 3x^2\ dx = x^3 + C[  /tex]
produces the graphic

For definite integrals, use the commands for subscripts and superscripts.

Code:
[tex]\int^1_0 x\ dx =0.5[  /tex]
produces the graphic

Modulus sign or absolute value

Use | for the modulus sign.

Code:
[tex]\sqrt{x^2} = |x|[  /tex]
produces the graphic

Factorial

Use the exclamation mark like normal.

Code:
[tex]3! = 6[  /tex]
produces the graphic

n choose r

Code:
[tex]^n\mathrm{C}_r[  /tex]
produces the graphic

Greek Letters

Write \x where x is the written form of the Greek letter (i.e. alpha, beta, gamma, ... , omega).

Code:
[tex]\pi[  /tex]
produces the graphic

Code:
[tex]\theta[  /tex]
produces the graphic

Infinity

To insert the infinity symbol, use \infty.

Code:
[tex]\infty[  /tex]
produces the graphic

Trigonometry

Code:
[tex]\cos \theta[  /tex]
produces the graphic

Code:
[tex]\sin \theta[  /tex]
produces the graphic

Code:
[tex]\tan \theta[  /tex]
produces the graphic

Code:
[tex]\sec \theta[  /tex]
produces the graphic

Code:
[tex]\mathrm{cosec} \theta[  /tex]
produces the graphic

Code:
[tex]\csc \theta[  /tex]
produces the graphic

Code:
[tex]\cot \theta[  /tex]
produces the graphic

Code:
[tex]\sin^2 \theta + \cos^2 \theta=1[  /tex]
produces the graphic

To write 'degrees', you could use the \circ command.

Code:
[tex]\cos 60^{\circ} = \frac{1}{2}[  /tex]
produces the graphic

Logarithms

Code:
[tex]\ln x^5 = 5 \ln x[  /tex]
produces the graphic

Code:
[tex]\log_{10} x^2 = 2 \log_{10} x[  /tex]
produces the graphic

Matrices

Code:
[tex]\begin{pmatrix} -2 & 6 & 7 \\2 & -5 & 1 \\1 & 2 & 3 \end{pmatrix}[  /tex]
produces the graphic

Determinants

Code:
[tex]\begin{vmatrix} -2 & 6 & 7 \\2 & -5 & 1 \\1 & 2 & 3 \end{vmatrix}[  /tex]
produces the graphic

vectors, simply write a matrix with only one column:

Code:
[tex]\begin{pmatrix} x \\ y \\ z \end{pmatrix}[  /tex]
produces the graphic

Code:
[tex]\vec{a}[  /tex]
produces the graphic

Limits

Code:
[tex]\displaystyle\lim_{x\to 0}[  /tex]
produces the graphic

Sets

Code:
[tex]\cup[  /tex]
produces the graphic

Code:
[tex]\cap[  /tex]
produces the graphic

Code:
[tex]\subset[  /tex]
produces the graphic

Code:
[tex]\subseteq[  /tex]
produces the graphic

Code:
[tex]\nsubseteq[  /tex]
produces the graphic

Code:
[tex]\in[  /tex]
produces the graphic

Code:
[tex]\not\in [  /tex]
produces the graphic

Code:
[tex]\mathbb{P}[  /tex]
produces the graphic

Code:
[tex]\mathbb{N}[  /tex]
produces the graphic

Code:
[tex]\mathbb{Z}[  /tex]
produces the graphic

Code:
[tex]\mathbb{I}[  /tex]
produces the graphic

Code:
[tex]\mathbb{Q}[  /tex]
produces the graphic

Code:
[tex]\mathbb{R}[  /tex]
produces the graphic

Code:
[tex]\mathbb{C}[  /tex]
produces the graphic

Code:
 gives
produces the graphic

Logic Symbols

Code:
[tex]\forall[  /tex]
produces the graphic

Code:
[tex]\land[  /tex]
produces the graphic

Code:
[tex]\lor[  /tex]
produces the graphic

Code:
[tex]\exists[  /tex]
produces the graphic

Code:
[tex]\neg[  /tex]
produces the graphic

Code:
[tex]\sim[  /tex]
produces the graphic
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