# Math Functions and Operations

### 1. Math basics

You’ll often need to define a mathematical expression when working with either the Data tool or Modeling. Mostly you’ll use the same
basic math operators as those you might use in a spreadsheet program or other electronic tools:

+ | Addition |

- | Subtraction |

* | Multiplication |

/ | Division |

^ | Power |

() | Parentheses to define order of operation |

Example: For an object dropped under the force of gravity at time t = 0 and initial y position = 0, its y position as a function of time
would be expressed by this equation (or one of its various equivalents):

y = (1/2)*ay*t^2 -or- y = (ay*t^2)/2

where the vertical acceleration (ay) = -9.81

Good practice: If you’re not sure how any electronic tool will apply order of operations, define that order properly using parentheses.

Beyond these basic operators, here are some of the more commonly-used functions available in Tracker:

- abs(a) will return the absolute value of a
- sqrt(a) will return the square root of a
- exp(a) is the same as e^a
- log(a) will return the natural logarithm of a
- log10(a) will return the logarithm of base 10 of a
- sin(a), cos(a), tan(a) will return the basic trigonometric functions in radians [NOT degrees]
- asin(a), acos(a), atan(a) are the reverse trigonometric functions

### 2. Additional functions

The following are special purpose functions that most students will rarely need, but they’re available if you ever DO need one of them:

- sign(a) will return -1 for negative numbers and 1 for positive numbers and 0
- max(a,b[,c…]) will return the maximum value from the list in parentheses
- min(a,b[,c…]) will return the minimum value from the list in parentheses
- fac(a) will return the factorial of a
- hypot(a[,b,c..]) will return the square root of the sum of the squares of the values in the list
- sinh(a), cosh(a), tanh(a) will return the basic hyperbolic functions
- asinh(a), acosh(a), atanh(a) are the reverse hyperbolic functions