Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for higher math students to grasp.
Initially, we are required to explain what radians are thereby you can see how this theorem is used in practice. Thereafter we’ll take it one step further by exhibiting some 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 means ray or nostril, and is a fundamental theory in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more frequently used unit in math.
In other words, radians and degrees are just two distinct units of measure used for measuring the same thing: angles.
Note: a radian is not to be mistaken with a radius. They are two entirely separate concepts. A radius is the length from the center of a circle to the border, while a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
We have two ways to think regarding this question. The initial method is to figure out about how many radians exists 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 easily:
π radians = 180 degrees
The second way to figure out about this question is to think about how many degrees exists in a radian. We all know that there are 360 degrees in a complete circle, and we also know that there are two pi radians in a full 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 helpful relying upon which you're trying to do.
How to Change Radians to Degrees?
Since we've covered what degrees and radians are, let's find out how to change them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known values to get your unknown values. For example, if you are required to convert .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 can be implemented both ways. Let’s recheck our workings 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 converted one type, it will always work with another unsophisticated calculation. In this case, after changing .785 from its original form back again, following these steps produced precisely what was predicted -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's attempt some examples, so these theorems become easier to digest.
Now, we will convert pi/12 rad into degrees. Just like previously, we will plug this value into the radians slot of the formula and solve 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 the answer! pi/12 radians equivalents 15 degrees.
Let's try one more general conversion and transform 1.047 rad to degrees. Yet again, use 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 exact).
Now, what to do if you are required to change degrees to radians?
By using the very same 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 work out with the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you recollect 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 a few 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 need to make a transformation among radians and degrees.
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