October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very crucial ability for progressive math students to understand.

First, we are required to define what radians are thereby you can perceive how this theorem is used in practice. Then we’ll take this a step further by showing a few examples of changing from radians to degrees quickly!

What Is a Radian?

Radians are measurement units for angles. It is originated from the Latin word "radix," which suggests nostril or ray, 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 used unit in math.

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

Note: a radian is not to be confused with a radius. They are two absolety different things. A radius is the length from the middle of a circle to the perimeter, though a radian is a unit of measure for angles.

Correlation Between Radian and Degrees

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

2π radians = 360 degrees

Or easily:

π radians = 180 degrees

The second way to think regarding this question is to consider how many degrees are present in a radian. We understand that there are 360 degrees in a whole circle, and we also know 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 depending on what you're trying to do.

How to Change Radians to Degrees?

Since we've gone through what degrees and radians are, let's find out how to change them!

The Formula for Converting Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

With ease put in your known values to get your unknown values. For instance, if you are required to turn .7854 radians into degrees, your proportion will be:

π radians.7854 radians = 180 degreesz degrees

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

This formula implied both ways. Let’s verify our operation by reverting 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

To work out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.

Now that we've converted one type, it will always work out with another simple calculation. In this scenario, afterwards converting .785 from its original form back again, after these steps produced exactly what was anticipated -45°.

The formulas plays out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Going From Radians to Degrees

Let's go through a few examples, so these concepts become simpler to digest.

At the moment, we will convert pi/12 rad into degrees. Just like before, 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 generally do:

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

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

Let's try some more 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).

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

By utilizing the very exact 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, put in the knowns and solve for 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 you have it! These are just some of the examples of how to convert radians to degrees and the other way around. Remember the equation and try solving for yourself the next time you need to make a transformation among radians and degrees.

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