Calculator for finding the Area of a circle
   
 There are a number of ways to measure angles
Related Chapters
   
 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:
1 = p radians

180°
 
 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 2p/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