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I had been wondering for a while why it is that we use the radian as the unit of angular measurement in higher sciences and mathematics (calculus, physics, engineering) as opposed to the degree.

In reviewing the relationship between the degree and radian, I believe that I have developed a decent understanding of them both and why radians are preferred. Perhaps I can receive some confirmation.

When we measure angles with degrees and radians, we are actually measuring twodifferentquantities.

The degree is a measure of how wide two rays are opened; the turn or rotation of a complete circle.

The radian is a ratio of a portion of a circle's arc length to its radius. If the radius of said circle is 1, then the radian is simply just the arc length. So in essence, when we perform angular measurement with the radian, we are not measuring the rotation around the circle, rather we are measuring the distance around the circle. If the radius of the circle is not 1, we can simply multiply radian by the radius to acquire the correct measurement.

To these ends, it would be more convenient to use radians as opposed to degrees.

Is this correct?

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# Why we measure angles with Radians

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