Problem 105

Question

Explain what is meant by one radian.

Step-by-Step Solution

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Answer

One radian is the angle created at the center of a circle when an arc equal in length to the radius is drawn on the circumference.

1Step 1: Definition

A radian is a unit of measure for angles used mainly in mathematics. It is defined in the context of a circle.

2Step 2: Experimentation

Imagine drawing a circle with a radius length of 1. Now draw an arc with that same length -- which will be also of length 1 -- along the circumference of the circle. The angle you have now created from the center of the circle to the two ends of the arc is equal to one radian.

3Step 3: Conceptual Understanding

Essentially, radian is the measurement of the angle created when we wrap the radius of a circle along the circumference. In different words, an angle of 1 radian is an angle at the center of the circle that subtends an arc on the circumference equal in length to the radius.

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