October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important ability for progressive mathematics students to comprehend.

First, we are required to explain what radians are so that you can see how this formula is used in practice. After that we’ll take this a step further by showing some examples of going from radians to degrees easily !

What Is a Radian?

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

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

That being said, radians and degrees are just two separate units of measure utilized for measuring the identical thing: angles.

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

Relationship Between Radian and Degrees

There are two manners to think about this question. The first way is to think about how many radians there are in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). Therefore, we can say:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The second way to figure out about this question is to consider how many degrees exists in a radian. We understand that there are 360 degrees in a full circle, and we also know that there are two pi radians in a complete 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 useful relying upon which you're trying to do.

How to Go From Radians to Degrees?

Now that we've went through what radians and degrees are, let's find out how to turn them!

The Formula for Changing Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

With ease plug in your given values to obtain your unknown values. For example, if you wished to change .7854 radians to degrees, your proportion will be:

π radians.7854 radians = 180 degreesz degrees

To work out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.

This formula works both ways. Let’s double-check our work by converting 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 transformed one type, it will always work with different unsophisticated calculation. In this scenario, after converting .785 from its original form back again, after these steps made precisely what was anticipated -45°.

The formulas plays out 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 ideas become simpler to digest.

At the moment, we will change pi/12 rad to degrees. Just like previously, we will place this number into the radians slot of the formula and solve 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 the answer! pi/12 radians equals 15 degrees.

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

Degrees = (180 * 1.047) / π

Yet again, you multiply and divide as fitting, and you will end up with 60 degrees! (59.988 degrees to be precise).

Right away, what happens if you want to transform 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 wish to change 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 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 a few examples of how to change radians to degrees and conversely. Keep in mind the formula and try it out for yourself the next time you have to make a conversion among radians and degrees.

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