Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential skill for progressive mathematics students to grasp.
Initially, we are required to specify what radians are so that you can see how this formula works in practice. Thereafter we’ll take it one step further by showing some examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which implies nostril or ray, and is a essential theory in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more commonly used unit in mathematics.
Simply put, radians and degrees are merely two distinct units of measure employed for measuring the identical thing: angles.
Note: a radian is not to be confused with a radius. They are two absolety separate things. A radius is the distance from the center of a circle to the edge, whereas a radian is a measuring unit for angles.
Association Between Radian and Degrees
There are two manners to go about regarding this question. The first way is to contemplate about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). Therefore, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to think regarding this question is to calculate how many degrees exists in a radian. We all know that there are 360 degrees in a full circle, and we also know that there are two pi radians in a complete circle.
If we divide each side by π radians, we’ll get that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful relying on what you're trying to do.
How to Go From Radians to Degrees?
Since we've went through what radians and degrees are, let's practice how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Simply put in your given values to derive your unknown values. For example, if you wanted to change .7854 radians to degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s recheck our workings by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Once we've changed one type, it will always work with another straightforward calculation. In this instance, afterwards converting .785 from its original form back again, following these steps created precisely what was expected -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's go through some examples, so these theorems become simpler to digest.
Now, we will transform pi/12 rad into degrees. Much like previously, we will plug this number in the radians slot of the formula and work it out it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. Once again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Right away, what to do if you want to change degrees to radians?
By using the very exact formula, you can do the opposite in a pinch by work out with radians as the unknown.
For example, if you have to change 60 degrees to radians, put in the knowns and work out with the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you recollect the formula to solve for radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to change radians to degrees and conversely. Keep in mind the equation and try it out for yourself the next time you are required to make a change between radians and degrees.
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