October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very crucial ability for advanced arithmetic students to grasp.

Initially, we are required to define what radians are thereby you can perceive how this formula works in practice. After that we’ll take it one step further by exhibiting a few examples of converting from radians to degrees with ease!

What Is a Radian?

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

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

In other words, radians and degrees are simply two separate units of measure utilized for measuring the identical thing: angles.

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

Association Between Radian and Degrees

There are two manners to go about about this question. The initial method is to think about how many radians exists in a full circle. A full circle is equals to 360 degrees or two pi radians (exactly). So, we can say:

2π radians = 360 degrees

Or easily:

π radians = 180 degrees

The second way to figure out about this question is to consider how many degrees are present in a radian. We all know 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 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 practice how to turn them!

The Formula for Giong From Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

With ease put in your known values to obtain your unknown values. For instance, if you are required to convert .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 works both ways. Let’s double-check our workings by changing 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.

Now that we've changed one type, it will always work out with another straightforward calculation. In this scenario, after converting .785 from its original form back again, ensuing 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 go through a handful of examples, so these theorems become simpler to digest.

At the moment, we will convert pi/12 rad into degrees. Just like before, we will plug this number into 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 it! pi/12 radians equals 15 degrees.

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

Degrees = (180 * 1.047) / π

Yet again, you multiply and divide as appropriate, and you will find yourself with 60 degrees! (59.988 degrees to be exact).

Now, what happens if you are required to change degrees to radians?

By using the very exact formula, you can do the converse in a pinch by solving it considering 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 equation to find radians, you will get the exact result:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

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

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