In addition to the basic arithmetic operations addition (+), subtraction (-), multiplication (*) and division (/), R has built-in standard mathematical functions. In the following section we take a look at some of them. Please note that in the course of this e-learning module we will encounter many more functions in R, we will even build user-defined functions by our own.

Absolute value function abs()

abs(3 - 12)

## [1] 9

Square root function sqrt()

sqrt(64)

## [1] 8

Exponentiation function exp()

exp(1)

## [1] 2.718282

log function (base \(e\)) log()

log(10)

## [1] 2.302585

log base 10 function log10()

log10(1000)

## [1] 3

Generally applicable: log function (base b) log(x, base = b)

log(81, base = 3)

## [1] 4

Mathematical constant \(\pi\)

pi

## [1] 3.141593

Trigonometric functions sine, cosine, tangent (argument in radians) sin(), cos(), tan()

sin(pi / 2)

## [1] 1

cos(pi / 2)

## [1] 6.123032e-17

tan(0)

## [1] 0

Inverse trigonometric functions arc-sine, arc-cosine, arc-tangent asin(), acos(), atan()

asin(0)

## [1] 0

acos(1)

## [1] 0

atan(pi)

## [1] 1.262627

 

Exercise: Check whether the cosine of 360° within the unit circle is 1!

### your code here

Show code

cos(2 * pi)

## [1] 1

 

Round x to n decimal places round(x,n)

round(pi, 2)

## [1] 3.14

Floor function (rounds down) floor()

floor(pi)

## [1] 3

Ceiling function (rounds up) ceiling()

ceiling(pi)

## [1] 4

 

Advanced Exercise: Consider Earth as a ball with a radius of 6371 km and calculate the distance between two meridians at the equator, 23 degree, 50 degree and 67 degree latitude. Round your answer to 1 decimal place! Bear in mind that the trigonometric functions in R expect angles in radians!

### your code here

Show code

latitudes <- c(0, 23, 50, 67)
# 1 degree = pi/180 rad
round((2 * pi * 6371) / 360 * cos((pi / 180) * latitudes), 1)

## [1] 111.2 102.4  71.5  43.4

 

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Citation

The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: Hartmann, K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.