Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for progressive math learners to understand.
First, we need to explain what radians are thereby you can see how this formula is used in practice. Then we’ll take it one step further by looking at a few examples of converting from radians to degrees with ease!
What Is a Radian?
Radians are units of measurement for angles. It comes from the Latin word "radix," which implies nostril or ray, and is a fundamental concept in geometry and mathematics.
A radian is the SI (standard international) unit for angles, even though a degree is a more frequently used unit in arithmetic.
Simply put, radians and degrees are merely 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 entirely distinct things. A radius is the length from the middle 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 about this question. The initial way is to contemplate about how many radians there are in a full circle. A full circle is equivalent 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 figure out about this question is to consider how many degrees exists in a radian. We understand 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 notice that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful depending upon which you're trying to get.
How to Convert Radians to Degrees?
Now that we've covered what degrees and radians are, let's find out how to turn 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
With ease plug in your given values to obtain your unknown values. For example, if you wished to change .7854 radians into degrees, your proportion would 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 can be implemented both ways. Let’s verify our work by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Now that we've converted one type, it will always work out with different unsophisticated calculation. In this instance, afterwards converting .785 from its original form back again, ensuing these steps produced perfectly 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 attempt some examples, so these concepts become simpler to digest.
Now, we will change pi/12 rad to degrees. Much like before, we will plug this value into 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 do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equals 15 degrees.
Let's try another general 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 fitting, and you will end up with 60 degrees! (59.988 degrees to be exact).
Right away, what happens if you want to transform degrees to radians?
By employing the very exact formula, you can do the contrary in a pinch by solving for radians as the unknown.
For example, if you wish 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 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 some of the examples of how to convert radians to degrees and the other way around. Remember the formula and see for yourself the next time you have to make a transformation between radians and degrees.
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