- 1). Multiply the measurement in degrees by the mathematical constant π, which equals 3.14. For the example, multiplying a 45 degree angle by π results in 45π.
- 2). Divide that number by 180, which is the number of degrees of a line. For the example 45π divided by 180 equals π/4.
- 3). Convert that into a decimal representation using a calculator. π/4 equals 0.785, rounded to the nearest thousandth. Both π/4 and 0.785 are acceptable answers for the measurement of the angle in radians and can be written as π/4 rad and 0.785 rad.
- 4). Divide the arc length by the radius to get the measurement of the angle in radians. The arc length is a set and finite segment of the circumference of the circle, and dividing it by the radius will give the measurement in radians. For example, if the arc length is 8 and the radius is 10, then the measurement of the angle is 0.8 rad.
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