Radians are used to measure angles. It is defined as the amount of distance covered along a circumference of a circle when an angle is rotated around the circumference’s centerline by that amount of distance. For example, if you had chosen any random angle on the unit circle below and traveled that same distance away from the centerline of that particular angle, then this would be 1 radian because one full revolution occured.
A full revolution would be 360 degrees so in this case, it was only 1 degree. If you moved another degree away from the centerline (360/2=180), you would have traveled 180cm so both examples cover 2 radians. There is no direct relationship between degrees and radians, however, there is one between radian and revolutions. For example, 2 revolutions would be the same as 360 degrees, but it would also be equal to 6.2radians because 6.2 x (360/2) = 6.2 x (180).
- Radians are handy converters in math, especially when converting them into fractions or decimals. Most significant numbers in mathematics usually come with decimal points or fractions of numbers which makes converting them into degrees more difficult for some people.
- Radians can also be used to measure angles on a unit circle by adding the correct angle measurements together.
- To convert an angle measurement from degrees to radian, one will need to multiply your degree measurement by pi/180
1 degree = pi/180 x 1 Radian
45 degrees = 45xpi/180 Radians
To convert an angle measurement from radians to degrees, you will need to multiply your radians by 180/pi(3.14) and then divide it by the total number of radians (ex: 2radians=2×3.14/6=0.52radians, 360degrees=360×3.14/6).
45radians = (45x 3.14)/6 Degrees
360 degrees(1 full rotation)=360×3. 14 / 6 Degrees (takes into account that one rotation is equal to 2 radians)
These formulas can be difficult for some people, and that’s why it’s best to learn the degrees and radians on a unit circle because most students learn better when they see visual examples of things rather than just reading formulas. When comparing radian measurement to degree measurements, keep in mind that there is no such thing as negative degrees so if you are using the equation to convert from degrees to radians, your number will always be positive(180degrees=3.14radians).
Properties of radians:
- There is no such thing as negative degrees because you can only move in one direction on the unit circle or 360degrees.
- You can add and subtract measurements in radians but multiplying them will result in a different measurement so it’s best to stay with one method of measuring angles especially when doing trigonometry.
- There are infinite numbers of angles you could measure with radians and each new angle is separated by pi/2 (90degrees), but when it comes to converting them into degrees, there is only one way mentioned earlier.
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A real-life example of radians:
If you were to drive around a circular race track without stopping, then each lap would be equal to 360degrees but it would also be an incomplete rotation which means that driving one full lap equals 2 radian. This is because there are two radians in a circle which means that the circumference of the track divided by the radius is equal to pi (3.14).
For example: If a race track was 100meters long and its radius was 50m, then the total length of the race track circumferential measurement would be 100x(3.14)/50 or 153.86meters back to front.
So, this was radian and conversion of degrees to radians. One can find many more fascinating concepts of mathematics on the Cuemath website. Cuemath is the best website for exploring and learning mathematics which offers excellent effectiveness and efficiency.