How do you convert #(8pi)/3# into degrees?

1 Answer
Prof Guillemette
Aug 3, 2015

we need to use #pi=180# to convert

Explanation:

#(8*pi)/3# is a radian measure which needs to be converted to degrees. For that we need a simple conversion factor: #pi=180#

Now we are going to setup an equation with the conversion factor. A nice way to do this is to take advantage of the proportionality of the problem. So we set the equations up like this:

#(8*pi)/3=x# in the same proportion as #pi=180#

#(8*pi)/3/pi=x/180#

we want to simplify this by changing the division to a multiplication

#(8*pi)/3*(1/pi)=x/180#

now we simplify the #pi/pi = 1#

#8/3=x/180#

to solve we simply undo the division on x with a multiply

#180*(8/3)=x#

#x=480#
(we changed the direction at the end to follow convention)

NOTE: always put the same units in the same fraction
#(rad)/(rad)=(degrees)/(degrees)#

and that makes us happy. :)

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