Why is a Circle 360 Degrees? It Actually Isn't...

We are always taught that a circle has 360 degrees, but have you ever thought why??? Why 360? What makes that number so special? And the truth is, it really is not that special. We could divide it however we want, but the most "mathematical" and "natural" way of getting the angle is by considering the arc length that is equal to the radius, and then having 2pi of those to give the circumference of the circle. The angle that makes that arc length equal to the radius is approximately 57 degrees, but we give it the name one radian, and therefore there are 2pi radians in the circle. This is a more natural way of defining an angle. We also go through a worked example question and see how working with radians can give simpler formulas for the area and perimeter of a sector. I hope you enjoy this video!
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Question taken from: CIE 9709 Summer 2023 Paper 12
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[@naveenpujani716]

I didnt understand the part where k came in. So how is alpha equal to k x theta

[@MathsWithMuza]

Great question! So we basically define alpha to be equal to a multiple of theta, ie k times theta. This is because any angle is going to be a multiple of 1 radian, which we said was the definition of theta. We can denote the multiple by some random letter k, and then eventually we realize that if k=1 then we get 1 times theta which is equal to theta (of course!), and use this to prove the further results. Let me know if this is still unclear!

[@naveenpujani716]

@MathsWithMuza Ahh okay okay. Thank you for this. Makes the video the best one now !!

[@MathsWithMuza]

Thanks glad we could clear it out!

[@hasnainabbas3970]

Excellent learning video