October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very important skill for higher arithmetic students to understand.

Initially, we are required to explain what radians are in order that you can see how this formula works in practice. Then we’ll take a further step by looking at a few examples of changing from radians to degrees with ease!

What Is a Radian?

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

A radian is the SI (standard international) measuring unit for angles, even though a degree is a more generally utilized unit in mathematics.

In other words, radians and degrees are merely two separate units of measure employed for measuring the same thing: angles.

Note: a radian is not to be mixed with a radius. They are two completely different things. A radius is the distance from the center of a circle to the border, while a radian is a measuring unit for angles.

Correlation Between Radian and Degrees

We have two manners to think about this question. The first method 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 (precisely). Hence, we can state:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The second way to figure out regarding this question is to think about how many degrees exists in a radian. We understand that there are 360 degrees in a whole 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 see that 1 radian is approximately 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

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

How to Go From Radians to Degrees?

Now that we've covered what radians and degrees are, let's find out how to convert them!

The Formula for Giong From Radians to Degrees

Proportions are a useful 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 instance, if you are required to turn .7854 radians into degrees, your proportion would 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 works both ways. Let’s verify our operation by converting 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

To solve for 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 instance, afterwards changing .785 from its original form back again, ensuing these steps created precisely what was predicted -45°.

The formulas work out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Converting Radians to Degrees

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

Now, we will change pi/12 rad to degrees. Much like before, we will put this value in 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 generally would:

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

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

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

Degrees = (180 * 1.047) / π

One more time, you multiply and divide as fitting, and you will find yourself with 60 degrees! (59.988 degrees to be precise).

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

By employing the very exact formula, you can do the converse in a pinch by solving it considering radians as the unknown.

For example, if you want to convert 60 degrees to radians, plug in the knowns and work out with 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 some of the examples of how to transform radians to degrees and conversely. Remember the formula and try solving for yourself the next time you have to make a transformation from or to radians and degrees.

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