Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for higher math students to comprehend.
First, we are required to explain what radians are so that you can understand how this theorem is used in practice. After that we’ll take it one step further by showing a few examples of going from radians to degrees easily !
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which implies nostril or ray, 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 arithmetic.
Simply put, radians and degrees are merely two distinct units of measure employed for measuring the identical thing: angles.
Note: a radian is not to be mistaken with a radius. They are two entirely distinct things. A radius is the distance from the center of a circle to the border, though 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 first method 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 (exactly). Hence, we can state:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The next way to figure out about this question is to think about how many degrees there are in a radian. We all know that there are 360 degrees in a full 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 do.
How to Go From Radians to Degrees?
Now that we've covered what degrees and radians are, let's find out how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for changing a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply put 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 find out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s recheck our operation by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Once we've transformed one type, it will always work out with another unsophisticated calculation. In this case, after converting .785 from its first form back again, ensuing these steps created perfectly what was anticipated -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 concepts become easier to digest.
At the moment, we will convert pi/12 rad to degrees. Just the same as before, we will plug 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 it! pi/12 radians equivalents 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
Once again, you multiply and divide as fitting, and you will end up with 60 degrees! (59.988 degrees to be almost exact).
Now, what to do if you want to change degrees to radians?
By using the very exact formula, you can do the opposite in a pinch by work out with radians as the unknown.
For example, if you want to convert 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 recollect the equation to find radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to transform radians to degrees and conversely. Bear in mind the formula and see for yourself the next time you need to make a transformation between radians and degrees.
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