



There are a number of ways to measure angles




other than with degrees. 





Another popular way is something called radians.






In an earlier chapter we talked about triangles on a coordinate grid. 


We set the hypotenuse equal to 1. 








And we said to
think of the hypotenuse like the hour hand on a watch. 


If you attach
a pencil on the end of the hypotenuse 


away from the origin [(0,0)
point] 


and moved the hypotenuse around like a clock hand, 


the pencil
will draw a circle: 











POP QUIZ! 


What is the
length of the line we just drew? 


The distance
around the circle is called the circumference. 


The equation
to find the length of the circumference is: 





Circumference =
2pr 


(r stands for
radius) 





In our circle,
the radius is 1, so the measure of the circumference is just 2p 





Radians are
the length of the arc at the outside edge of the circle 


in units
that are the length of the radius. 











Since the distance all the way around the circle in radians is 2p,



and
it is also 360°, we can say: 





360°
= 2 p
radians 


Which
also means 


180°
= p
radians 


And
we can also write this as: 








So
if we should want to convert something from radians to degrees 


or
degrees to radians, we just use this and do a unit conversion. 





Examples: 





Change
60°
to radians: 





60° 
x 
p
radians

= 
60°
x p
radians 
= 
p 
radians 



180° 
180° 
3 






Change
^{2}^{p}/3
radians to degrees: 





2p
radians 
x 
180° 
= 
180°
x 2p
radians 
= 
120° 



3 
p
radians 
3p
radians 






Remember
that p
is just a number. It is about 3.14159. 


You could replace the
p's
in your answers with the decimal approximations, 


but most of the
time it's better to leave the p
in the answer. 





Most
of the time a radian measure has a p
in it, but it doesn't have to. 





Examples: 





Change
4 radians to degrees: 





4
radians 
x 
180° 
= 
180°
x 4
radians 
= 
720° 
= 
229.18° 



p
radians 
p
radians 
3.14159 






copyright 2008 Bruce Kirkpatrick

