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Radians are easy!

Radians are a measure of angle. If you measure the length of the radius (R) of a circle on its circumference, the angle that that arc makes at the center of the circle is 1 radian.


The circumference of a circle is 2 pi R so as the length on the circumference of each radian is R, it follows that 2 pi radians will cover the circumference. The number of degrees to cover the circumference is 360, so 360 degrees = 2 pi radians. It's easier to remember 180 degrees = pi radians. So in degrees, 1 radian = 180/ pi = approximately 57.3 degrees (for checking, that's almost 60 degrees!)


To convert degrees to radians multiply by pi and divide by 180. To convert radians to degrees multiply by 180 and divide by pi.


The most common radian measures are:

  • pi = 180 degrees

  • pi/2 = 90 degrees

  • pi/3 = 60 degrees

  • pi/4 = 45 degrees

  • pi/6 = 30 degrees


Adding radians? Easy. As an example, add 90 degrees to 60 degrees. That's pi/2 + pi/3 = 5 pi/6 Check it! pi radians = 180 degrees, so that's 180 * 5/6 = 150 degrees. Sounds right!

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