Radians: Difference between revisions

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{{EmphasisBox|<b>This article is about an advanced topic.</b>|red|dark=yes}}
{{EmphasisBox|<b>This article is about an advanced topic.</b>|red|dark=yes}}


This is a very basic explanation of [http://en.wikipedia.org/wiki/Radian Radians], if you have never been taught Radians before.
This is a very basic explanation of [http://en.wikipedia.org/wiki/Radian Radians], if you have never been taught Radians before.
Line 5: Line 6:
Radians are another way of describing angles, as opposed to using degrees.  Something similar to Radians is used in everyday life, when we use fractions.  We say, "I want a third of a piece of cake," not, "I want 120 degrees worth of cake."
Radians are another way of describing angles, as opposed to using degrees.  Something similar to Radians is used in everyday life, when we use fractions.  We say, "I want a third of a piece of cake," not, "I want 120 degrees worth of cake."


In this sense, we are using the concept of "[[http://en.wikipedia.org/wiki/Turn_(geometry) turns]]". There is one turn in a full circle, so 1 turn is 160&deg;. It follows that 180&deg; is half a turn, 90&deg; is a quarter turn, and so on.
In this sense, we are using the concept of "[http://en.wikipedia.org/wiki/Turn_(geometry) turns]". There is one turn in a full circle, so 1 turn is 360&deg;. It follows that 180&deg; is half a turn, 90&deg; is a quarter turn, and so on.


==Conversion==
==Conversion==


One turn is equal to 2[[pi|π]] radians. Therefore, 2[[pi|π]] radians = 360&deg;. From this, formulae for converting degrees to radians, and vice versa, can be found:
One turn is equal to 2{{pi}} radians. Therefore, 2{{pi}} radians = 360&deg;. From this, formulae for converting degrees to radians, and vice versa, can be found:


[[Image:Radians_to_Degrees.png]]
[[Image:Radians_to_Degrees.png]]
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[[Image:Degrees_to_Radians.png]]
[[Image:Degrees_to_Radians.png]]


==...==
In Lua terms, these can be written as:
 
{{lua|=
local radians = degrees * math.pi / 180
local degrees = radians * 180 / math.pi
}}
 
However, there is a cleaner way of doing this. Lua provides functions to do these conversions for you in the math library:
{{lua|=
local inRadians = math.rad(degrees)
local inDegrees = math.deg(radians)
}}
 
==Radians and Degrees==


For a basic idea of Radians to how much "cake" or "circle" you have, divide the radians by "2 pi".  To convert how much "cake" or "circle" you have to Radians, multiply the "cake" (or circle) by "2 pi":
For a basic idea of Radians to how much "cake" or "circle" you have, divide the radians by "2 pi".  To convert how much "cake" or "circle" you have to Radians, multiply the "cake" (or circle) by "2 pi":
Line 22: Line 36:
! Angle in radians !! represents
! Angle in radians !! represents
|-
|-
| 2[[pi|π]] || one whole circle
| 2{{pi}} || one whole circle
|-
|-
| [[pi|π]] || one-half circle
| {{pi}} || one-half circle
|-
|-
| 2[[pi|π]]/3 || one-third circle
| 2{{pi}}/3 || one-third circle
|-
|-
| pi/2 || one fourth circle
| {{pi}}/2 || one fourth circle
|-
|-
| 2pi/5 || one-fifth circle
| 2{{pi}}/5 || one-fifth circle
|-
|-
| pi/3 || one-sixth circle
| {{pi}}/3 || one-sixth circle
|-
|-
| 2pi/7 || one-seventh circle
| 2{{pi}}/7 || one-seventh circle
|-
|-
| pi/4 || one-eighth circle
| {{pi}}/4 || one-eighth circle
|-
|-
| 2pi/9 || one-ninth circle
| 2{{pi}}/9 || one-ninth circle
|-
|-
| pi/5 || one-tenth circle
| {{pi}}/5 || one-tenth circle
|-
|-
| 2pi/11 || one-eleventh circle
| 2{{pi}}/11 || one-eleventh circle
|-
|-
| pi/6 || one-twelfth circle
| {{pi}}/6 || one-twelfth circle
|-
|-
| 0 || No circle
| 0 || No circle
|}
|}


[http://en.wikipedia.org/wiki/Degree_%28angle%29 Degrees] slice a circle into 360 parts -- and sometimes degrees need to be converted into Radians.  To convert from degrees to radians, divide by (180/pi).  To convert from radians to degrees, multiply by (180/pi).   
[http://en.wikipedia.org/wiki/Degree_%28angle%29 Degrees] slice a circle into 360 parts -- and sometimes degrees need to be converted into Radians.  To convert from degrees to radians, divide by (180/pi).  To convert from radians to degrees, multiply by (180/{{pi}}).   


For example:<br>
For example:<br>
360 Degrees || 2pi radians<br>
270 Degrees || 3pi/2 radians<br>
180 Degrees || pi radians<br>
90 Degrees || pi/2 radians<br>
60 Degrees || pi/3 radians<br>
45 Degrees || pi/4 radians<br>
30 Degrees || pi/6 radians<br>
0 Degrees || 0 radians<br>
== Advanced ==
The above examples have used whole numbers and rather clean fractions.  Unfortunately, if you want to make something like a "spiralling staircase", you will need to work with much finer "pie slices" than the ones above, and you will get decimals.  However, the principle and the computation is the same:
For example:
{|
{|
! Degrees !! Radians
! Angle in degrees !! represents
|-
|-
| 0 || 0
| 360&deg; || 2{{pi}} radians
|-
|-
| 1 || 0.017453292519943295769236907684886
| 270&deg; || 3{{pi}}/2 radians
|-
| 2 || 0.034906585039886591538473815369772
|-
|-
| 3 || 0.052359877559829887307710723054658
| 180&deg; || {{pi}} radians
|-
|-
| 4 || 0.069813170079773183076947630739545
| 90&deg; || {{pi}}/2 radians
|}
 
And the reverse:<br>
{|
! Radians !! Degrees
|-
|-
| 1 Radian || 57.295779513082320876798154814105
| 60&deg; || {{pi}}/3 radians
|-
|-
| 2 Radians || 114.59155902616464175359630962821
| 45&deg; || {{pi}}/4 radians
|-
|-
| 3 Radians || 171.88733853924696263039446444232
| 30&deg; || {{pi}}/6 radians
|-
|-
| 4 Radians || 229.18311805232928350719261925642
| 0&deg; || 0 radians
|}
|}


And so on.  You can convert Degrees to Radians and Radians to Degrees using [http://www.10ticks.co.uk/radianConverter.aspx online conversion tools], with your calculator, or with the following functions:
== More info==
 
You can convert Degrees to Radians and vice versa using [http://www.10ticks.co.uk/radianConverter.aspx online conversion tools], with your calculator, or with the following members of the Lua [[Function_Dump/Mathematical_Functions|math library]]:
 
=== [[Function_Dump/Mathematical_Functions#math.rad(x)|math.rad(x)]] ===
 
Converts x (in degrees) into Radians. Example: math.rad(90) results in  1.5707963267949.
 
=== [[Function_Dump/Mathematical_Functions#math.deg(x)|math.deg(x)]] ===


math.pi<br>
Converts x (in Radians) into degrees. Example: math.deg(3.1415926535898) results in 180.
Roblox reads this as Pi, which is 3.141592654.<br>


math.rad (x)<br>
=== [[Function_Dump/Mathematical_Functions#math.pi|math.pi]] ===
Converts x (in degrees) into Radians. Example: math.rad(90) results in  1.5707963267.<br>


math.deg (x)<br>
Roblox reads this as Pi, which is 3.1415926535898.
Converts x (in Radians) into degrees. Example: math.deg(3.141592654) results in 180.<br>


== See Also ==
== See Also ==


*[[Function_Dump/Mathematical_Functions]]
*[http://en.wikipedia.org/wiki/Radian Radians]
*[http://en.wikipedia.org/wiki/Radian Radians]
*[http://en.wikipedia.org/wiki/Degree_%28angle%29 Degrees]
*[http://en.wikipedia.org/wiki/Degree_%28angle%29 Degrees]
*[http://www.10ticks.co.uk/radianConverter.aspx Radian Degree Converter]
*[http://www.10ticks.co.uk/radianConverter.aspx Radian Degree Converter]
*[http://en.wikipedia.org/wiki/Table_of_polyhedron_dihedral_angles Table of polyhedron dihedral angles]
*[http://en.wikipedia.org/wiki/Table_of_polyhedron_dihedral_angles Table of polyhedron dihedral angles]

Latest revision as of 20:54, 14 April 2012

This article is about an advanced topic.


This is a very basic explanation of Radians, if you have never been taught Radians before.

Radians are another way of describing angles, as opposed to using degrees. Something similar to Radians is used in everyday life, when we use fractions. We say, "I want a third of a piece of cake," not, "I want 120 degrees worth of cake."

In this sense, we are using the concept of "turns". There is one turn in a full circle, so 1 turn is 360°. It follows that 180° is half a turn, 90° is a quarter turn, and so on.

Conversion

One turn is equal to 2π radians. Therefore, 2π radians = 360°. From this, formulae for converting degrees to radians, and vice versa, can be found:

File:Radians to Degrees.png

In Lua terms, these can be written as: 

local radians = degrees * math.pi / 180
local degrees = radians * 180 / math.pi

However, there is a cleaner way of doing this. Lua provides functions to do these conversions for you in the math library: 

local inRadians = math.rad(degrees)
local inDegrees = math.deg(radians)

Radians and Degrees

For a basic idea of Radians to how much "cake" or "circle" you have, divide the radians by "2 pi". To convert how much "cake" or "circle" you have to Radians, multiply the "cake" (or circle) by "2 pi":

Angle in radians represents
2π one whole circle
π one-half circle
2π/3 one-third circle
π/2 one fourth circle
2π/5 one-fifth circle
π/3 one-sixth circle
2π/7 one-seventh circle
π/4 one-eighth circle
2π/9 one-ninth circle
π/5 one-tenth circle
2π/11 one-eleventh circle
π/6 one-twelfth circle
0 No circle

Degrees slice a circle into 360 parts -- and sometimes degrees need to be converted into Radians. To convert from degrees to radians, divide by (180/pi). To convert from radians to degrees, multiply by (180/π).

For example:

Angle in degrees represents
360° 2π radians
270° 3π/2 radians
180° π radians
90° π/2 radians
60° π/3 radians
45° π/4 radians
30° π/6 radians
0° 0 radians

More info

You can convert Degrees to Radians and vice versa using online conversion tools, with your calculator, or with the following members of the Lua math library:

math.rad(x)

Converts x (in degrees) into Radians. Example: math.rad(90) results in 1.5707963267949.

math.deg(x)

Converts x (in Radians) into degrees. Example: math.deg(3.1415926535898) results in 180.

math.pi

Roblox reads this as Pi, which is 3.1415926535898.

See Also

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