Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for progressive math learners to grasp.
Initially, we are required to explain what radians are so that you can see how this theorem works in practice. After that we’ll take it one step further by showing some examples of going from radians to degrees quickly!
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 critical idea in mathematics and geometry.
A radian is the SI (standard international) unit for angles, although a degree is a more generally utilized unit in math.
That being said, radians and degrees are just two separate units of measure used for measuring the identical thing: angles.
Note: a radian is not to be mixed with a radius. They are two completely different things. A radius is the length from the center of a circle to the edge, though a radian is a measuring unit for angles.
Relationship Between Radian and Degrees
There are two ways to go about regarding this question. The first method is to contemplate about how many radians there are in a full circle. A full circle is equals to 360 degrees or two pi radians (exactly). So, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to think regarding this question is to calculate how many degrees there are in a radian. We all know that there are 360 degrees in a whole circle, and we also understand 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 approximately 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 Change Radians to Degrees?
Since we've gone through what degrees and radians are, let's practice how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a helpful tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Simply plug in your known values to obtain your unknown values. For instance, if you are required to turn .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s verify our work by reverting 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 out with another unsophisticated calculation. In this instance, after converting .785 from its original form back again, ensuing 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 go through a few examples, so these theorems become simpler to digest.
At the moment, we will transform pi/12 rad to degrees. Just the same as previously, we will place this number 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 normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equals 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. One more time, utilize the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as fitting, and you will find yourself with 60 degrees! (59.988 degrees to be precise).
Right away, what to do if you are required to transform degrees to radians?
By utilizing the very exact formula, you can do the converse in a pinch by solving it considering radians as the unknown.
For example, if you wish to transform 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 memorized the equation to solve for 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. Bear in mind the equation and try it out for yourself the next time you need to make a conversion among radians and degrees.
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