October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important skill for progressive math students to understand.

Initially, we need to define what radians are so that you can perceive how this theorem is used in practice. After that we’ll take this a 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 comes from the Latin word "radix," which implies nostril or ray, and is a critical theory in geometry and mathematics.

A radian is the SI (standard international) unit of measurement for angles, even though a degree is a more frequently used unit in mathematics.

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

Note: a radian is not to be mixed with a radius. They are two entirely different concepts. A radius is the length from the middle of a circle to the perimeter, while a radian is a measuring unit for angles.

Correlation Between Radian and Degrees

We have two ways to think about this question. The first method is to think about how many radians exists in a full circle. A full circle is equivalent to 360 degrees or two pi radians (exactly). Therefore, we can say:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The next way to think about this question is to think about how many degrees exists in a radian. We understand that there are 360 degrees in a complete 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 notice that 1 radian is about 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are beneficial relying on what you're trying to get.

How to Convert Radians to Degrees?

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

The Formula for Giong From Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

Simply put in your known values to obtain your unknown values. For instance, if you wanted to turn .7854 radians into 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 can be implemented both ways. Let’s double-check our work 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 changed one type, it will always work with different unsophisticated calculation. In this scenario, after changing .785 from its first form back again, following these steps made precisely 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 try a handful of examples, so these theorems become easier to digest.

Now, we will convert pi/12 rad into degrees. Just like previously, we will put this value in the radians slot of the formula and calculate 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 equivalents 15 degrees.

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

Degrees = (180 * 1.047) / π

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

Now, what happens if you want to transform degrees to radians?

By employing the very same formula, you can do the contrary in a pinch by solving for radians as the unknown.

For example, if you wish to change 60 degrees to radians, put 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 identical answer:

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 vice versa. Remember the equation and see for yourself the next time you have to make a change from or to radians and degrees.

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