Why is pi = 180 degrees radians?

1 Answer
May 14, 2015

Think of a circle.
Now think of half of it and focus on the crust or contour of it: What is its length? Well if an entire circle is #2pi*r# half will be only #pi*r# but half a circle corresponds to #180°# ok...Perfect....
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and here the difficult bit:
radians is: (arc length)/(radius)
Your arc length, for half circle, we saw that was #pi*r# dividing by #r#...you get #pi# radians!!!!!!

Is it clear?...probably not...