October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very essential skill for higher arithmetic students to grasp.

First, we are required to define what radians are so that you can understand how this formula is used in practice. Then we’ll take a further step by exhibiting some 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 nostril or ray, and is a fundamental concept in geometry and mathematics.

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

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

Note: a radian is not to be confused with a radius. They are two completely distinct things. A radius is the distance from the middle of a circle to the perimeter, while a radian is a unit of measure for angles.

Relationship Between Radian and Degrees

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

2π radians = 360 degrees

Or easily:

π radians = 180 degrees

The next way to figure out about this question is to calculate how many degrees are present in a radian. We all know that there are 360 degrees in a whole circle, and we also understand that there are two pi radians in a full circle.

If we divide each side by π radians, we’ll see 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?

Now that we've gone through what radians and degrees are, let's learn how to turn them!

The Formula for Converting Radians to Degrees

Proportions are a useful tool for converting a radian value to degrees.

π radiansx radians = 180 degreesy degrees

Just put in your known values to get your unknown values. For example, if you are required to convert .7854 radians into 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 can be implemented both ways. Let’s recheck 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.

Once we've converted one type, it will always work with different simple calculation. In this scenario, afterwards converting .785 from its first form back again, ensuing these steps made exactly what was predicted -45°.

The formulas work out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Converting Radians to Degrees

Let's try some examples, so these ideas become easier to digest.

At the moment, we will convert pi/12 rad into degrees. Just like before, we will put this number into the radians slot of the formula and calculate 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 result! pi/12 radians equivalents 15 degrees.

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

Degrees = (180 * 1.047) / π

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

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

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

For example, if you have to convert 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 recollect the equation to solve for 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 convert radians to degrees and the other way around. Bear in mind the equation and try it out for yourself the next time you need to make a conversion among radians and degrees.

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