Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for advanced math learners to grasp.
Initially, we need to specify what radians are in order that you can see how this theorem works in practice. After that we’ll take a further step by looking at a few examples of changing from radians to degrees easily !
What Is a Radian?
Radians are units of measurement for angles. It comes from the Latin word "radix," which implies ray or nostril, and is a essential idea in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, while a degree is a more generally utilized unit in math.
Simply put, radians and degrees are simply two distinct units of measure utilized for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two absolety distinct things. A radius is the distance from the center of a circle to the border, though a radian is a measuring unit 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 second way to think about this question is to consider how many degrees there are in a radian. We know that there are 360 degrees in a complete 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 approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are useful depending on what you're trying to do.
How to Convert Radians to Degrees?
Since we've covered what radians and degrees are, let's find out how to convert them!
The Formula for Changing Radians to Degrees
Proportions are a useful tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known values to get your unknown values. For instance, if you wanted to change .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To solve for z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s recheck our workings by converting 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 changed one type, it will always work with another straightforward calculation. In this case, afterwards changing .785 from its original form back again, following these steps created precisely what was expected -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 go through some examples, so these ideas become easier 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 solve 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 equivalents 15 degrees.
Let's try another general conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as appropriate, and you will wind up with 60 degrees! (59.988 degrees to be precise).
Right away, what to do if you want to convert degrees to radians?
By utilizing the very same formula, you can do the contrary in a pinch by work out with radians as the unknown.
For example, if you wish to transform 60 degrees to radians, plug 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 find radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just handful of examples of how to transform radians to degrees and vice versa. Keep in mind the formula and try solving for yourself the next time you are required to make a transformation among radians and degrees.
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