Radians

Definition: A radian (rad) is a unit of angle measure based on a circle’s radius.

When the radius of a circle is equal in length to the measure of an arc, the central angle that inscribes it is equal to 1 radian:

radians.jpg

There are 2π radians in a circle, which tells us:

1 radian = 360°/2π ≈ 57.29°

Example: How many radians make up 3/5 of a circle?

Solution:

Keeping in mind that there are 2π radians in a circle, we can multiply 2π * (3/5) to determine the number of radians in 3/5 of a circle:

2π * (3/5) = 6/5π radians

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