October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very essential skill for advanced math students to understand.

Initially, we are required to explain what radians are in order that you can perceive how this formula is used in practice. Thereafter we’ll take this a step further by looking at some examples of going 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 ray or nostril, and is a critical concept in geometry and mathematics.

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

Simply put, radians and degrees are simply two different units of measure utilized for measuring the identical thing: angles.

Note: a radian is not to be mistaken with a radius. They are two absolety separate things. A radius is the distance from the middle of a circle to the edge, though a radian is a measuring unit for angles.

Correlation Between Radian and Degrees

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

2π radians = 360 degrees

Or easily:

π radians = 180 degrees

The next way to figure out about this question is to calculate how many degrees are present in a radian. We understand that there are 360 degrees in a whole circle, and we also recognize 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 about 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are useful depending upon which you're trying to do.

How to Change Radians to Degrees?

Since we've went through what degrees and radians are, let's practice how to change them!

The Formula for Giong From Radians to Degrees

Proportions are a beneficial tool for turning a radian value to degrees.

π radiansx radians = 180 degreesy degrees

Simply put in your given values to obtain your unknown values. For instance, if you wished 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 implied both ways. Let’s recheck our operation 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.

Since we've changed one type, it will always work with another simple calculation. In this case, after changing .785 from its first form back again, following these steps made exactly what was anticipated -45°.

The formulas solves like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Changing Radians to Degrees

Let's attempt a few examples, so these ideas become easier to digest.

Now, we will change pi/12 rad to degrees. Much like previously, we will plug this value into the radians slot of the formula and calculate it like this:

Degrees = (180 * (π/12)) / π

Now, let divide and multiply as you usually would:

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

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

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

Degrees = (180 * 1.047) / π

One more time, you multiply and divide as suitable, and you will wind up with 60 degrees! (59.988 degrees to be precise).

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

By employing the very same formula, you can do the opposite 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 solve for the unknowns:

60 degrees = (180 * z radians) / π

(60 * π)/180 = 1.047 radians

If you remember the formula to solve for 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 conversely. Bear in mind the equation and see for yourself the next time you are required to make a conversion among radians and degrees.

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