Degrees, Rads, and Coterminal Angles

Degrees can't be left with a decimal. They have to be broken down into minutes (') and seconds (")
To Convert to minutes and seconds:

• to convert to minutes multiply what is behind the decimal in degrees by 60.


• to convert to seconds multiply what is behind the decimal in minutes by 60. If you get a decimal for your seconds just drop everything on the right side of the decimal.


• to convert minutes and seconds to degrees you use the formula:

degrees+(minutes/60)+(seconds/3600)

Radians are the preferred way to measure angels every formula require radians

To Convert to Radians:

• to convert from degrees to radians you use the formula:

degrees x (pi/180)= rads

(type in the degrees/180 in your calculator and convert to a fraction and put the pi beside it)

• to convert from radians to degrees you use the formula:

rads x 180/pi ( the pi should cancel out)

Ex 1: Convert 100.96 degrees to minutes and seconds

• .96 x 60 =57.6 minutes


• .6 x 60 = 36 seconds


• 100 degrees 57 minutes 36 seconds

Ex 2: Convert 50 degrees 30 minutes 36 seconds to degrees

• 50 + 30/60 + 36/3600 =50.51 degrees

Ex 3: Convert 214 degrees to radians

• 214 x pi/180 = 107/90 pi

Ex 4: Convert 5pi/3 to degrees

• 5pi/3 x 180/pi= 900/3 = 300