![]() ![]() Since 45 degrees is 1/8 of a circle, if you divide 2π by 8, you get π/4. You can perform the same trick with 45 degrees. But, do you see how we started counting π/6 radians until we completed the full circle of 2π radians? Let’s reduce those that are can be reduced, and rewrite things like 5×π/6 as 5π/6. Now, the majority of these can be reduced. Let’s look at the same angles, multiples of 30 degrees, written in radians. If we divide 2π radians by 12, we will have the equivalent of 30 degrees, in radians. And, do you see that we get nearly EVERY single angle when we approach this with multiples of 30º?Ī full circle divided into equal groups of 12 is 30 degrees. This doesn’t make much sense because we easily know what 4 × 30 is, so we just write 120.īut, when we use radians, with exact numbers, this becomes a very handy approach. If we count 30 degrees repeatedly until we get around the circle, we have 12 angles. You can try to memorize, or you can use a basic division/counting trick. The Unit Circle: You may be required to know the conversions of radians into degrees for the angles on the Unit Circle, and may have to do so without a calculator. That’s typically the easiest way to solve a proportion. ![]() Since we’re converting to radians, we want radians to be in the numerator of our ratio. Let’s see a couple of examples for the sake of clarity. (A proportion is made from equal ratios.) Depending on what it is you’re converting to, set up one of the following. The ratio we will use comes from the fact that a full circle of rotation is 360° and also 2π radians. One radian of rotation is approximately 57.3°.Ĭonverting Between Radians and Degrees: The most consistent way to convert between radians and degrees is with a proportion. So one radian is how far along the circumference the length of one radius would be. One radian is an arc length the same distance as the radius, made by a central angle.Ī radian, which sounds quite similar to radius, is the length along the circumference of the radius. This makes sense because of where the number π originates. In short, if you take the distance of the radius, and make it into a curve, and wrap it around the circumference of the circle, you get 2π radians. Radians are similar in that they measure rotation, but have a relationship with the radius of a circle. If you’re facing your bedroom window and you spin around completely so that you’re again facing your window, you’ve rotated 360 degrees. So, 2π radians is actually an irrational number, approximately 6.28 radians.Ī degree is defined such that in a full rotation there are 360 degrees. Other SI units are meters, kilograms, and seconds. SI stands for (basically) system international. Background Information: Radians are the SI units used to measure angles. ![]()
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