How do you turn 72 degree into radians?

2 Answers
Oct 17, 2015

Multiply. 72 x (#pi#/180)


= 72 x #pi#/180

Hence 72 degrees in radians is 2#pi#/5 or = 1.26, correct to three significant figures.

Oct 17, 2015

Shoaib Hameed method is correct but I wish to expand on his solution


It is a matter of ratios between radians and degrees:

The main point of reference is that there are #pi# radians in #180^0#.

Your question requires an answer in radians so we would express our reference ratio in the form of #"radians"/"degrees"#. Your target type is always written as a numerator as it is a more efficient calculation method. The next step:

As there is a direct link between the number of radians to its associated number of degrees we can write:

#(pi " radians")/( 180^0 " degrees") = ( "unknown radians")/("given degrees")#

So we end up with:

#( "unknown radians") = (pi " radians")/( 180^0 " degrees") times ("given degrees")#