October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important ability for higher mathematics students to comprehend.

Initially, we need to define what radians are in order that you can understand how this formula is used in practice. Then we’ll take a further step by exhibiting a few examples of changing from radians to degrees quickly!

What Is a Radian?

Radians are measurement units for angles. It is originated from the Latin word "radix," which means ray or nostril, and is a fundamental idea in geometry and mathematics.

A radian is the SI (standard international) unit of measurement for angles, while a degree is a more generally used unit in math.

Simply put, radians and degrees are simply two different units of measure employed for measuring the same thing: angles.

Note: a radian is not to be mistaken with a radius. They are two absolety different concepts. A radius is the length from the middle of a circle to the edge, while a radian is a measuring unit for angles.

Association Between Radian and Degrees

We have two manners to go about regarding this question. The initial way is to think 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 simply:

π radians = 180 degrees

The second way to think about this question is to think about how many degrees are present in a radian. We know that there are 360 degrees in a full circle, and we also recognize that there are two pi radians in a complete 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 helpful relying upon which you're trying to get.

How to Go From Radians to Degrees?

Since we've gone through what radians and degrees are, let's practice how to convert them!

The Formula for Changing Radians to Degrees

Proportions are a helpful tool for turning a radian value to degrees.

π radiansx radians = 180 degreesy degrees

Just put in your known values to obtain your unknown values. For example, if you wished to convert .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 implied both ways. Let’s double-check our operation by converting 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

To find out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.

Since we've changed one type, it will always work with another unsophisticated calculation. In this case, afterwards converting .785 from its first form back again, following these steps produced precisely what was predicted -45°.

The formulas plays out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Changing Radians to Degrees

Let's try a handful of examples, so these ideas become easier to digest.

At the moment, we will change pi/12 rad into degrees. Just the same as previously, we will put 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 the answer! pi/12 radians equals 15 degrees.

Let's try one more 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 fitting, and you will end up with 60 degrees! (59.988 degrees to be precise).

Now, what happens if you want to change degrees to radians?

By employing the very same formula, you can do the converse in a pinch by solving it considering radians as the unknown.

For example, if you want to change 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 remember the formula to solve for radians, you will get identical answer:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

And there you have it! These are just a few examples of how to convert radians to degrees and vice versa. Remember the formula and try solving for yourself the next time you are required to make a change from or to radians and degrees.

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