Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for advanced arithmetic learners to grasp.
Initially, we need to specify what radians are so that you can perceive how this theorem is used in practice. Thereafter we’ll take this a step further by looking at a few examples of going from radians to degrees with ease!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which means nostril or ray, and is a essential theory in geometry and mathematics.
A radian is the SI (standard international) unit for angles, while a degree is a more frequently used unit in math.
Simply put, radians and degrees are just two separate units of measure employed for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely distinct concepts. A radius is the length 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 ways to think regarding this question. The first way is to figure out about how many radians are present in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). So, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to figure out regarding this question is to consider how many degrees there are in a radian. We understand that there are 360 degrees in a complete 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 about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are useful relying on what you're trying to do.
How to Go From Radians to Degrees?
Now that we've gone through what degrees and radians are, let's practice how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a useful tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just put in your given values to obtain your unknown values. For instance, if you wanted to change .7854 radians into degrees, your proportion will 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 implied both ways. Let’s recheck our work by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find out the value of y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Once we've converted one type, it will always work out with different simple calculation. In this case, afterwards converting .785 from its original form back again, ensuing 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 Converting Radians to Degrees
Let's attempt a handful of examples, so these theorems become simpler to digest.
At the moment, we will transform pi/12 rad to degrees. Just like previously, we will place this value in the radians slot of the formula and solve it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you generally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equivalents 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. Yet again, use the formula to get started:
Degrees = (180 * 1.047) / π
Once again, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you want to transform degrees to radians?
By employing the very exact formula, you can do the converse in a pinch by work out with radians as the unknown.
For example, if you have to transform 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 memorized the formula to solve for radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just handful of examples of how to convert radians to degrees and conversely. Remember the equation and see for yourself the next time you need to make a change from or to radians and degrees.
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