October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important ability for progressive arithmetic learners to grasp.

First, we need to define what radians are thereby you can see how this formula works in practice. Thereafter we’ll take this a step further by exhibiting a few examples of converting from radians to degrees quickly!

What Is a Radian?

Radians are units of measurement for angles. It is derived from the Latin word "radix," which means 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 commonly used unit in math.

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

Note: a radian is not to be mixed with a radius. They are two entirely separate things. A radius is the length from the center of a circle to the edge, while a radian is a unit of measure for angles.

Relationship Between Radian and Degrees

We have two ways to go about regarding this question. The initial way is to think about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). Therefore, we can state:

2π radians = 360 degrees

Or easily:

π radians = 180 degrees

The next way to think regarding this question is to consider how many degrees exists in a radian. We know 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 relying on what you're trying to get.

How to Change Radians to Degrees?

Now that we've gone through what degrees and radians are, let's practice how to change 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 given values to get your unknown values. For example, if you wished to change .7854 radians into degrees, your proportion would 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 implied both ways. Let’s verify our work by changing 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.

Since we've changed one type, it will always work out with different unsophisticated calculation. In this instance, after changing .785 from its first form back again, after these steps created exactly what was predicted -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 handful of examples, so these ideas become simpler to digest.

At the moment, we will convert pi/12 rad to degrees. Much like before, we will plug this number in the radians slot of the formula and solve it like this:

Degrees = (180 * (π/12)) / π

Now, let divide and multiply as you usually do:

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

There you have it! pi/12 radians equivalents 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

Once again, you multiply and divide as suitable, and you will end up with 60 degrees! (59.988 degrees to be exact).

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

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

For example, if you want to transform 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 equation to find radians, you will get the exact result:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

And there you have it! These are just handful of examples of how to change radians to degrees and the other way around. Bear in mind the equation and see for yourself the next time you are required to make a change among radians and degrees.

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