October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important skill for advanced arithmetic students to understand.

First, we are required to specify what radians are in order that you can understand how this formula is used in practice. After that we’ll take it one step further by looking at some examples of converting from radians to degrees with ease!

What Is a Radian?

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

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

In other words, radians and degrees are just two different units of measure used for measuring the identical thing: angles.

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

Correlation Between Radian and Degrees

We have two ways to go about regarding this question. The initial method is to think about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). Therefore, we can say:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The second way to think regarding this question is to think about how many degrees there are in a radian. We understand that there are 360 degrees in a full 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 useful depending upon which you're trying to get.

How to Go From Radians to Degrees?

Now that we've went through what radians and degrees are, let's practice how to change them!

The Formula for Giong From Radians to Degrees

Proportions are a useful tool for changing a radian value into degrees.

π radiansx radians = 180 degreesy degrees

Simply plug in your known values to derive your unknown values. For instance, if you wanted to change .7854 radians into degrees, your proportion will 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 double-check our operation by changing 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.

Since we've converted one type, it will always work out with another straightforward calculation. In this instance, afterwards converting .785 from its first form back again, ensuing these steps made perfectly what was expected -45°.

The formulas solves like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Converting Radians to Degrees

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

At the moment, we will transform pi/12 rad to degrees. Just like previously, we will place this value into the radians slot of the formula and calculate it like this:

Degrees = (180 * (π/12)) / π

Now, let divide and multiply as you usually would:

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

There you have it! pi/12 radians equivalents 15 degrees.

Let's try another common conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:

Degrees = (180 * 1.047) / π

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

Now, what to do if you are required to convert degrees to radians?

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

For example, if you wish to transform 60 degrees to radians, plug in the knowns and solve for the unknowns:

60 degrees = (180 * z radians) / π

(60 * π)/180 = 1.047 radians

If you remember the equation to find radians, you will get the exact result:

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 conversely. Keep in mind the formula and see for yourself the next time you are required to make a change among radians and degrees.

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