How do you convert #(5pi)/7# from radians to degree?

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Answer 1 · 2018-05-22T10:08:04

#128.57...#

Remember that #pi# radians are #180°#, so you can build the following proportion, if #r# is the angle in radians and #d# is the angle in degree:

#r:pi = d:180#

From here, isolate #d#:

#d = r*180/pi#

So, plugging #r=(5pi)/7#, we have

#d = (5cancel(pi))/7*180/cancel(pi) = \frac{5\cdot 180}{7} = \frac{900}{7} = 128.57...#

Answer 2 · 2018-05-22T10:11:19

It is #900^{\circ}/7#

From #alpha^{\circ}/alpha=360^{\circ}/(2*pi)# we get
#alpha^{\circ}=180^{\circ}/pi*5/7*pi#
canceling the #pi# we get
#alpha^{\circ}=900^{\circ}/7#