An angle of 1 radian is the angle subtended by an arc with the same length as the radius shown below.
Conversions between radians and degrees
Arc Length
The formula to find the arc length is illustrated below:
Here, r is the radius and θ is the angle in radians.
If you had to find the arc length of a sector with a radius of 5cm and an angle of 80°, you would answer the question using this method - shown below.
Area of a Sector
The area of a sector can be found using this formula.
If we had to find the area of the sector in the previous example, we would use a method like this.
I remember in high school thinking that I'll never get to use these formulas ever again. Boy was I wrong. I use the circle formula way too often when I'm helping program games with my friends. Good thing that my high school teacher was persistent with me until I learned it.
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It is nice to know that maths still serves you to this day.
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