October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

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

First, we are required to define what radians are so that you can understand how this theorem is used in practice. Thereafter we’ll take it one step further by exhibiting 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 theory in mathematics and geometry.

A radian is the SI (standard international) measuring unit for angles, although a degree is a more generally used unit in arithmetic.

In other words, radians and degrees are just two different units of measure utilized 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 center of a circle to the edge, though a radian is a measuring unit for angles.

Correlation Between Radian and Degrees

We have two ways to go about about this question. The first way is to contemplate about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (precisely). So, we can state:

2π radians = 360 degrees

Or easily:

π radians = 180 degrees

The second way to think regarding this question is to calculate how many degrees exists 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 whole circle.

If we divide each side by π radians, we’ll get that 1 radian is about 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are helpful depending on what 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 convert them!

The Formula for Converting Radians to Degrees

Proportions are a beneficial tool for changing a radian value to degrees.

π radiansx radians = 180 degreesy degrees

With ease plug in your given values to get your unknown values. For example, if you are required to convert .7854 radians to degrees, your proportion will 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 verify our work by changing 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

To solve for 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 straightforward calculation. In this case, afterwards changing .785 from its first form back again, after these steps made precisely what was expected -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 go through some examples, so these ideas become easier to digest.

Now, we will transform pi/12 rad to degrees. Just like before, we will place this value 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 generally would:

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

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

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

Degrees = (180 * 1.047) / π

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

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

By using the very same formula, you can do the contrary in a pinch by solving for 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 formula to solve for radians, you will get the exact result:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

And there it is! These are just handful of 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 conversion from or to radians and degrees.

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