Radians vs. Degrees | Where Do Radians Come From?
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You’re probably used to measuring circles in degrees. Another way to measure circles is RADIANS.
When your arc length is the same length as your radius…let’s pretend the radius = 1… we call that angle measure a radian.
If we were to continue to take that measure around, guess what half the circle equals….3.14159……..PI!
So when we measure circles this way, π = 180° or half the circle.
If we continued to measure around, a full circle (360°) would be 6.283185…. or 2π
So this translates to all angles such as π/2 = 90°
If this seems weird or hard to remember, think of the formula to find circumference. C = 2πr. If r =1, then we’re just left with C = 2π.
But what is the radius isn’t 1? Well, it is a proportion and will simplify down, no matter what the radius is. Just like every circle is 360° when we measure in degrees…Every circle is 2π radians when we measure in radians.
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#midnightmathtutor #radians #degrees #circles
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