### Using the formula editor: Working with symbols

### Working with symbolic expressions

Mathematical formulas consist of more than just numbers: usually there are symbols present. Think of variables, names of physical quantities, names of functions, etcetera. To enter a mathematical formula you can use a keyboard and/or the formula editor. The table below lists the most common mathematical symbols and the syntax for entering them.

Symbol |
Syntax |
#\phantom{x}# Description |

\(\cos(x)\) | cos(x) |
#\phantom{x}# cosine of \(x\) |

\(\sin(x)\) | sin(x) |
#\phantom{x}# sine of \(x\) |

\(\tan(x)\) | tan(x) |
#\phantom{x}# tangent of \(x\) |

\(\ln(x)\) | ln(x) |
#\phantom{x}# natural logarithm of \(x\) |

\(\log_{a}(x)\) | log(a,x) or log_a(x) |
#\phantom{x}# logarithm of \(x\) with base \(a\) |

\(x^y\) | x^y |
#\phantom{x}# \(x\) to the power \(y\) |

\(e^x\) | e^x or exp(x) |
#\phantom{x}# \(e\)-power of \(x\), exponential function |

\(\sqrt{x}\) | sqrt(x) or rt(x,2) |
#\phantom{x}# square root of \(x\) |

\(\sqrt[n]{x}\) | rt(x,n) |
#\phantom{x}# \(n\)-th root of \(x\) |

\(|x|\) | abs(x) |
#\phantom{x}# absolute value of \(x\) |

\(\displaystyle \frac{x}{y}\) | x/y |
#\phantom{x}# \(x\) divided by \(y\) |

\(x\cdot y\) | x*y |
#\phantom{x}# product of \(x\) and \(y\) |

\(\pi\) | pi |
#\phantom{x}# the constant \(\pi\) |

There are a few things you should pay special attention to. The main rule is:

**Almost always use the multiplication sign * **

The only exception to the above rule is when an integer is followed by a letter or known symbol such as in \(2x\) and \(2\pi\).

`xy` is a name consisting of two characters; `x*y` is the product of two variables.`x2` is a name consisting of a letter followed by a number; x*2 is the product of a variabele and a number.

By the way, the system often warns its user when names consisting of two letter are entered:

Also in case of brackets it is often necessary to enter a multiplication symbol:

So not `2(x+1)` and`(x+1)x`, but `(x+1)*x` to denote a factorized expression.

`f(x-1)` usually indicates a function call with argument `x-1`, but it can also be read as a product of `f` and `x-1`; in case of `f*(x-1)`, there is no doubt anymore, because this is certainly a product.