Most people begin measuring angles in degrees. \u00a0However, you can also measure an angle in radians. \u00a01 rad\u224857.3\u00b0.<\/p>\n
While degrees come from (I am told) Babylonia, or one of the ancient civilizations of that area, radians are a “natural” way to measure angles. \u00a0Behold:<\/p>\n
![\"\"](\"..\/radian0.png\")
\nIn the above picture, CA is a radius. The arc from A to B is the same length as CA. Therefore, angle ACB is 1 radian. 1 radian is the angle that you traverse by following an arc the length of the radius. Said another way, it’s the angle subtended by an arc one radius long.<\/p>\n
Recall that the circumference of the circle is 2\u03c0r, where r is the radius. \u00a0Since 2\u03c0r is the exact circumference, 2\u03c0 radians is exactly 360\u00b0.<\/p>\n
Radians can be referred to as rads, but are usually stated without any unit. That’s how you can tell which way the angle is measured: \u00a0if it’s in degrees, it will have a degree sign. \u00a0If it’s in rads, it won’t have any units. \u00a0Therefore, an angle of 54\u00b0 means, of course, 54 degrees. \u00a0However, an angle of\u00a032 means 32 rads.<\/p>\n
Please keep enjoying this fine summer!<\/p>\n