many of friend are offered to thinking of a circle in regards to degrees: 360° is the totality circle. 180° is half the one etc... Well, radian measure is simply a different method of talking about the circle. Radian measure up is just different unit the measure.

simply as we can measure a football ar in yards or feet -- we have the right to measure a one in levels (like the an excellent old days) or in radians (welcome to the big leagues!)

Think about what words radian sound like... Well, it sounds choose "radius", right? It transforms out that a radian has a close connection to the radius the a circle.




You are watching: Rewrite each angle in radian measure as a multiple of π

therefore what is a radian then?

Definition that radian:

a radian is the measure of an edge that, when drawn as a main angle of a circle, intercepts one arc whose length is equal to the size of the radius the the circle.

This meaning is much easier construed by looking at the demonstration immediately below.


Demonstration of Radian that Circle


The gif below is an computer animation of 1 radian. An alert how the size of 1 radius stretches out to a portion of the circle. That section is 1 radian that the circle.


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