(eli5) whats the difference in radians and degrees (pls give real life examples)
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Degrees measure the angle of an object in relation to another object, for example, a level. Radians measure angle of an object based on the arc lenght travelled by the angle. 1 radian is equal to the circle radius.
This is your homework isn’t it?
If you draw a quarter circle with a radius of 10cm, the arc that you draw will be 15.7cm long. A radius of 20cm, an arc of 31.4cm. Radius of 1m, arc of 1.57m. In a quarter circle, the ratio between the arc and the radius is always 1.57. Therefore we say that a quarter circle has an angle of 1.57 (or π/2, to be exact) radians.
For degrees, we simply divide the full circle into 360 equal parts (6*60; the idea goes back to the Ancient Babylonians who were really into the number 6). So a half circle would be 180° and a quarter circle 90°.
The reason to use radians is that some mathematical stuff gets easier. For example, for very small angles, the sine of the angle is approximately equal to the value of the angle *in radians*. On the other hand, degrees give you nice numbers for simple geometrical objects; a right angle is 90° and an equilateral triangle 60°.
If you cut a circle into 360 equal pieces down the middle. 1 degree would be the angle of one of those pieces.
We decided to cut circles into 360 pieces for cultural and historical reasons, not anything particularly mathematical.
If you drew a line on the edge that was the same distance as the the edge is from the center of the circle (the radius). Then drew two lines from the ends to the center. The angle from the middle would be 1 radian.
Notice how we defined everything in that without pulling a number out of nowhere?
That’s the sort of thing mathematicians really like.
On the surface, they’re just two different ways of measuring angles. It’s like asking what’s the difference between feet and meters…they both measure lengths, one’s just bigger than the other one.
However. Degrees are kind of arbitrary. We decided to chop up a circle into some number of units and ended up choosing 360 (read other comments here for how/why that particular number). Which is fine but there’s nothing particularly mathematically profound about 360, it’s just convenient.
Radians, on the other hand, aren’t arbitrary…they’re very specifically chosen so that an angle of one radian in a circle has an arc length that’s exactly as long as the radius of the circle. This probably *sounds* arbitrary but, from a math/physics standpoint, it’s *far* more fundamental than a degree. Among other things, it grossly simplifies the math behind rotational motion and everything that uses rotational-type math (which is more than you might think). If you work in degrees you constantly have to carry conversion factors around, if you work in radians it’s the “natural” angle that falls out of other math and it all just works without having to keep track of units. This is why pretty much all physics/engineering works in radians. The only thing degrees are good for are navigation and geometry.
Degree = a circle’s circumference / 360.
Radian = a circle’s circumference / by it’s radius.
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