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 are required to specify what radians are in order that you can understand how this theorem is used 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 measurement units for angles. It comes 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) unit for angles, although a degree is a more generally utilized unit in mathematics.

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 mixed with a radius. They are two completely different concepts. A radius is the length 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 think regarding this question. The first method is to figure out about how many radians exists in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). So, we can state:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The next way to think regarding this question is to consider how many degrees exists in a radian. We all know that there are 360 degrees in a full circle, and we also recognize that there are two pi radians in a complete 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 upon which you're trying to do.

How to Change Radians to Degrees?

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

The Formula for Converting Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

With ease plug in your given values to obtain 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 work out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.

This formula can be implemented both ways. Let’s recheck our workings 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.

Since we've changed one type, it will always work with another simple calculation. In this instance, afterwards changing .785 from its original form back again, ensuing 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 try some examples, so these concepts become simpler to digest.

At the moment, we will transform pi/12 rad into degrees. Much like previously, we will put 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 would:

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

There you have it! 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 fitting, and you will find yourself with 60 degrees! (59.988 degrees to be exact).

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

By using the very exact formula, you can do the opposite in a pinch by work out with radians as the unknown.

For example, if you have to change 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 recollect the equation to find 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 a few examples of how to transform radians to degrees and conversely. Keep in mind the equation and try it out for yourself the next time you have to make a change from or to radians and degrees.

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