2 Radians

An angle measured as 2 radians.

Description

This figure illustrates the angle measured as radians. Note, the figure shows the numeric tic marks for radians, however it is standard practice to use the circle constant (tau) where as shown below. This abstraction makes the system much easier to use in practice.

Radian Angle System
Figure 1: Radian Angle System

Geometric Interpretation

The angle corresponding to radians is visualized by the circle below. Geometrically, the angle is equal to traveling the length of the radius twice along the circumference of the circle. As shown below, the abstract length denotes the length of the radius.

2 Radians Circle Radius 1

Note, we are using the radius to measure the angle formed on the circle, but the actual value of the radius does not matter. For example, the angle of radians is visualized using the circle of radius and the circle of radius shown below:

2 Radians Circle Radius 2 2 Radians Circle Radius 3

In the first circle of radius , to measure the angle of radians we travel radii of length along the circumference for a total of units. In the second circle, to measure the angle of radians we travel radii of length along the circumference for a total of units. In both cases, the measured angle is equal to multplied by the radius of the circle, which is why we refer to the angle as radians.

Resources

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