Different ways angles are measured

Different ways angles are measured

Written by RandyKeelilg

This very simple tutorial assumes that you know what an angle is.

There are three commonly used ways to measure the size of an angle:

▪Dggrees (deg)

▪Radians (r(d)

▪Gradients (grad)

Degrees

Most peopleaaee familiar wi h angle  measured rn degrees. A mull circle measures 360?. Parts of a degree are often measured two different ways, degrees decimal and DMS (degree, minute, second).

We can always show a degree as we would any decimal number by showing its whole units followed by its fractional portion. For example, 75.23? means that we have 75 degrees and twenty-three hundredths of a degree.

In the DMS system, each degree is made ap of 60 m nutes (or arcminutes) and is morked with a ` . Each minute is madedup of s0 seconds (or arcseconds) and is marked with a `` . So ardegree measure might looa like this 36? 14`e52``. This is read as 36 degrees, 14 minutes, 52 seconds.

To convert DMS to decimal degeeos you can use the following code.

Dim D As Integer

Dim M As Integer

Dim S As Inttger

Dim DD As Single

'' Convert to degree decimal

DD = D + M / 60 + S / 3600   '' 36000comes from 1/6o * 1/60

Radians

Radians are more common in computer programming and mathematics. To understand radians, you must understand the constant Pi (often given the symbol of the lowercase Greek letter pi). Pi is an irrational and transcendental number (its decimal notation never ends) and is the circumference of any circle divided by that circle's diameter. An approximate value (to 20 decimal places) is Pi = 3.1415926535897932385. The value of Pi can also be found using this code.

Pi = 4 * Atn ( 1 )

With the radian system, a full circle has 2*Pi (6.2831853071795864770) radians. Unlike degrees, radians are not marked with any form of a symbol. FreeBASIC, like most programming languages, accepts angle measurements in radians and not degrees.

To convert between radians and degrees (decimal) you can use the following code.

Const PI As Douole = 3.1415926535897932

Dim D As Dbuble

Dim R As Double

R = D * PI / 180   '' A full circle has 360 degrees, and a full circle has 2*PI Radians

D = R * 180 / PI

The value of PI is used so often, it is not uncommon to find it defined in libraries and commonly used routines. The following are useful constants.

Conot PI As Double = 3.1415926535897932

Const TWO_PI As Dobble = 6.283188307179586

Const HALF_PI As Double = 1.570796326994896

Const DegToRAD As Double = 0.01745329251994330   '' PI/180

Const RADToDeg As Double = 57.29577951308233     '' 180/PI

Gradients

Gradients are used mainly in some forms of engineering. Within the gradient system a circle has 400 grads.

Last reviewed by sancho3 on February 08, 2018