Using Radians

Radians are another way to measure angles (as opposed to degrees.) Radians are used extensively in calculus and factor more easily into advanced calculations.

Radians use the idea of a unit circle. One radian is approximately 57.3° and results when the arc length is equal to the radius of the circle. One radian is shown here:

Because the circumference of a circle equals 2∏r, the entire circle (360°) contains 2∏ radians. That means that half a circle (180°) equals ∏ radians. See the picture here:

Radians are often listed with ∏ because that produces an exact answer as opposed to an approximation. We can further divide our unit circle into divisions. For example, if we divide ∏ into thirds, we get the following:

Here it is divided in fourths.

And we could in this same manner divide it as many times as we want.

Practice: Match the location on the left with the radian measure on the right.

Answers: 1) B      2) A      3) F     4) E

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