October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important skill for advanced math learners to comprehend.

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

What Is a Radian?

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

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

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

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

Correlation Between Radian and Degrees

We have two manners 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). Hence, we can state:

2π radians = 360 degrees

Or simply:

π radians = 180 degrees

The second way to think about this question is to think about how many degrees there are 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 complete circle.

If we divide each side by π radians, we’ll get that 1 radian is approximately 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

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

How to Change Radians to Degrees?

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

With ease put in your known values to obtain your unknown values. For instance, if you are required to change .7854 radians to degrees, your proportion will 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 workings by changing 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.

Once we've changed one type, it will always work out with different simple calculation. In this instance, afterwards converting .785 from its first form back again, ensuing these steps produced perfectly 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 few examples, so these concepts become easier to digest.

At the moment, we will transform pi/12 rad to degrees. Just like before, we will plug 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 do:

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

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

Let's try one more common conversion and transform 1.047 rad to degrees. Yet 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 precise).

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

By utilizing the very same formula, you can do the contrary in a pinch by solving it considering radians as the unknown.

For example, if you have to convert 60 degrees to radians, put in the knowns and work out with the unknowns:

60 degrees = (180 * z radians) / π

(60 * π)/180 = 1.047 radians

If you recollect the equation to find 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 transform radians to degrees and vice versa. Keep in mind the equation and see for yourself the next time you are required to make a transformation from or to radians and degrees.

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