What is 7pi in degrees?

3 Answers
Jun 26, 2018

#7pi" radians" = color(blue)(1260^circ)#

Explanation:

Background:
The circumference of a circle gives the number of radians (number of segments of length equal to the radius) in the circumference. That is a "radian" is the length of the circumference divided by the length of the radius.

Since the circumference (#C#) is related to the radius (#r#) by the formula
#color(white)("XXX")C=pi2r#
#color(white)("XXXXXXXX")rArr # a single radian = #C/r=2pi#

In term of degrees, a circle, by definition, contains #360^circ#

Relating these two, we have
#color(white)("XXX")2pi ("radians") = 360^circ#
or
#color(white)("XXX")pi ("radians") =180^circ#

Therefore
#color(white)("XXX")7pi ("radians")=7xx180^circ=1260^circ#

Jun 26, 2018

#pi=180^@#, so #7pi=1260^@#.

Explanation:

#7pi*180^@/pi#
#(7cancel(pi)180^@)/cancel(pi)#
#7*180^@=1260^@#

Jun 26, 2018

#1260^@#

Explanation:

From our definition of a radian, we know

#pi# rad=#color(blue)(180^@)#

To convert #7pi# to degrees, we multiply what's in blue by #7#:

#color(red)7color(blue)(pi)# rad=#color(red)7*color(blue)(180)=1260^@#

Therefore, #7pi# rad is equal to #1260^@#.

Hope this helps!