Can anyone thoroughly explain Radian and Degree Measure as like a lesson in Pre-Cal?
A circle has 360 degrees, or 2π radians. (That’s 2*pi, in case your web browser doesn’t render it properly). That means that a half-circle is 180 degrees or π radians, and a quarter circle is 90 degrees or π/2 radians. People usually talk about degrees because that’s the units we’re raised in, but radians are actually more convenient for a lot of things. That’s because 2π*r is the formula for the circumference of the circle. In fact, we can generalize that to say that the length of the arc of part of a circle is the angle (measured in radians) times the radius. So if we have a half circle (π radians), the circular arc is π*r. And an arc of exactly 1 radian has the outside arc equal to r; that is, the radius and the length of the arc are the same. The angle isn’t particularly interesting expressed in degrees. It’s about 57.2957795 degrees, which isn’t very important except to let you convert between radians and degrees. It becomes even more important when you get to trigonometry. The fo
