Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for higher mathematics students to comprehend.
Initially, we need 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 a few examples of going from radians to degrees with ease!
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which means ray or nostril, and is a fundamental concept in geometry and mathematics.
A radian is the SI (standard international) unit for angles, although a degree is a more frequently utilized unit in mathematics.
That being said, radians and degrees are simply two different units of measure employed for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two completely different things. A radius is the length from the center of a circle to the border, whereas a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
There are two manners to go about about this question. The initial method is to contemplate about how many radians are present in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). So, we can state:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to think regarding this question is to think about how many degrees there are in a radian. We know that there are 360 degrees in a whole circle, and we also know that there are two pi radians in a whole 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 on what you're trying to get.
How to Change Radians to Degrees?
Since we've went through what radians and degrees are, let's find out how to convert them!
The Formula for Giong From Radians to Degrees
Proportions are a beneficial tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
With ease put in your given values to get your unknown values. For example, if you wished to convert .7854 radians into 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 works both ways. Let’s double-check our operation by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Now that we've changed one type, it will always work with different straightforward calculation. In this case, afterwards changing .785 from its first form back again, ensuing these steps created precisely what was predicted -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's attempt some examples, so these concepts become simpler to digest.
At the moment, we will transform pi/12 rad to degrees. Just the same as before, we will put this value 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 usually would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equals 15 degrees.
Let's try another common conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as suitable, and you will end up with 60 degrees! (59.988 degrees to be almost exact).
Now, what to do if you have to transform degrees to radians?
By employing the very exact formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you wish to transform 60 degrees to radians, plug in the knowns and solve for the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you remember 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 a few examples of how to change radians to degrees and the other way around. Remember the equation and try solving for yourself the next time you need to make a transformation among radians and degrees.
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