Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for higher arithmetic students to comprehend.
Initially, we are required to define what radians are so that you can perceive how this formula works in practice. Thereafter we’ll take this a step further by showing some examples of changing from radians to degrees easily !
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a essential idea in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, although a degree is a more generally utilized unit in math.
In other words, radians and degrees are just two distinct units of measure utilized for measuring the identical thing: angles.
Note: a radian is not to be mistaken with a radius. They are two entirely separate concepts. A radius is the distance from the middle of a circle to the edge, whereas a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
There are two manners to think regarding this question. The initial way is to figure out about how many radians are present in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). Therefore, we can say:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The next way to think about this question is to consider how many degrees exists in a radian. We understand that there are 360 degrees in a complete circle, and we also recognize that there are two pi radians in a complete circle.
If we divide each side by π radians, we’ll see that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial relying upon which you're trying to do.
How to Change Radians to Degrees?
Now that we've gone through what degrees and radians are, let's find out how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a beneficial tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your given values to obtain your unknown values. For instance, if you are required to change .7854 radians to degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To solve for z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula can be implemented both ways. Let’s double-check our work by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Since we've converted one type, it will always work out with different simple calculation. In this case, afterwards changing .785 from its original form back again, after these steps produced perfectly what was expected -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's attempt a handful of examples, so these concepts become simpler to digest.
Now, we will change pi/12 rad to degrees. Just the same as previously, we will plug this value into the radians slot of the formula and solve 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 equals 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. One more time, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as appropriate, and you will wind up with 60 degrees! (59.988 degrees to be exact).
Right away, what to do if you have to change degrees to radians?
By using the very same formula, you can do the converse in a pinch by work out with radians as the unknown.
For example, if you want to change 60 degrees to radians, put in the knowns and solve for the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you remember the equation to find radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to convert radians to degrees and vice versa. Keep in mind the formula and try it out for yourself the next time you are required to make a change among radians and degrees.
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