October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important skill for progressive mathematics learners to comprehend.

Initially, we are required to specify what radians are in order that you can see how this theorem is used in practice. Thereafter we’ll take this a step further by exhibiting some examples of converting from radians to degrees with ease!

What Is a Radian?

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

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

Simply put, radians and degrees are merely two separate units of measure utilized for measuring the same thing: angles.

Note: a radian is not to be confused with a radius. They are two entirely different things. A radius is the distance from the center of a circle to the edge, while a radian is a measuring unit for angles.

Association Between Radian and Degrees

We have two manners to think regarding this question. The initial way is to think about how many radians exists in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). So, we can say:

2π radians = 360 degrees

Or simply:

π radians = 180 degrees

The next way to figure out regarding this question is to consider how many degrees there are in a radian. We know that there are 360 degrees in a whole 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 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 relying upon which you're trying to get.

How to Change Radians to Degrees?

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

The Formula for Changing Radians to Degrees

Proportions are a beneficial tool for converting 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 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 with .7854 and divide by 3.14 (pi): 45 degrees.

This formula implied both ways. Let’s recheck our operation by reverting 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.

Now that we've converted one type, it will always work with another simple calculation. In this instance, after changing .785 from its original form back again, after these steps produced exactly what was predicted -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 a few examples, so these ideas become simpler to digest.

Now, we will change pi/12 rad into degrees. Just like before, we will put this value 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 normally would:

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

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

Let's try one more common 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).

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

By using the very exact formula, you can do the contrary in a pinch by work out with 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 memorized the formula to solve for radians, you will get the same thing:

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 vice versa. Bear in mind the equation and see for yourself the next time you are required to make a transformation between radians and degrees.

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