October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important skill for advanced math students to grasp.

First, we are required to define 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 looking at a few examples of going from radians to degrees quickly!

What Is a Radian?

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

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

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

Note: a radian is not to be mixed with a radius. They are two completely separate concepts. A radius is the distance from the middle of a circle to the perimeter, though a radian is a measuring unit for angles.

Correlation Between Radian and Degrees

There are two ways to go about about this question. The first method 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 (exactly). Therefore, we can say:

2π radians = 360 degrees

Or simply:

π radians = 180 degrees

The second way to figure out about this question is to think about how many degrees are present in a radian. We know that there are 360 degrees in a complete 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 notice that 1 radian is approximately 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are beneficial relying upon which you're trying to get.

How to Go From Radians to Degrees?

Since we've went through what radians and degrees are, let's learn how to turn them!

The Formula for Changing Radians to Degrees

Proportions are a helpful tool for converting a radian value into degrees.

π radiansx radians = 180 degreesy degrees

Just plug in your known values to get your unknown values. For instance, if you are required to turn .7854 radians to degrees, your proportion will 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 recheck our work by changing 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 changed one type, it will always work with different unsophisticated calculation. In this instance, after changing .785 from its first form back again, ensuing these steps made exactly what was expected -45°.

The formulas plays out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Going From Radians to Degrees

Let's go through a handful of examples, so these concepts become simpler to digest.

At the moment, we will convert pi/12 rad into 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 do:

Degrees = (180 * (π/12)) / π = 15 degrees.

There you have the answer! pi/12 radians equals 15 degrees.

Let's try another general conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:

Degrees = (180 * 1.047) / π

Once again, you multiply and divide as appropriate, and you will wind up with 60 degrees! (59.988 degrees to be exact).

Right away, what to do if you are required to change degrees to radians?

By utilizing the very exact formula, you can do the opposite in a pinch by solving for radians as the unknown.

For example, if you have 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 formula to find radians, you will get identical answer:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

And there it is! These are just some of the examples of how to change radians to degrees and conversely. Bear in mind the equation and try solving for yourself the next time you are required to make a change between radians and degrees.

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