#could someone explain what this paragraph is saying?
tropic jewel
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halcyon dagger
Well, basically, you define one radian as such an angle that the arc with this angle has the same length as its radius.
tropic jewel
oh ok so in this phot what is the difference with one radian angle measure being the same as the the length of one radius on the arc?
Also I don't understand what that last sentence is talking about
halcyon dagger
oh ok so in this phot what is the difference with one radian angle measure being...
Well, basically, we can define angles greater than 2π and less than 0. For that, you start winding around the circle from the positive x-direction. Counterclockwise turning makes a positive angle, while clockwise turning makes a negative angle.
tropic jewel
Well, basically, we can define angles greater than 2π and less than 0. For that,...
oh ok and also why is the arc length the same as the angle measure in radians in the unit circle and is that the same for all circles like the one in the previous photo?
halcyon dagger
oh ok and also why is the arc length the same as the angle measure in radians in...
The arc length is its radian angle measure times its radius.
So, L = θr.
tropic jewel
oh so thats why the radian angle measure and the arc length is the same for the unit circle but for example a circle with radius 2 wouldn't have an arc the same as its radian angle measure so if the angle was 2 radians then the length for the arc would be 4?
halcyon dagger
oh so thats why the radian angle measure and the arc length is the same for the ...
Yes.