October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

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

Initially, we need to specify what radians are in order that you can perceive 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 easily !

What Is a Radian?

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

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

In other words, radians and degrees are just two different units of measure used 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 length from the middle of a circle to the perimeter, while a radian is a unit of measure for angles.

Association Between Radian and Degrees

There are two ways to go about about this question. The first way is to think about how many radians are present in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). So, we can state:

2π radians = 360 degrees

Or simply:

π radians = 180 degrees

The next way to figure out about this question is to calculate how many degrees exists in a radian. We know that there are 360 degrees in a whole circle, and we also recognize that there are two pi radians in a whole 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 beneficial depending on what you're trying to get.

How to Convert Radians to Degrees?

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

The Formula for Giong From Radians to Degrees

Proportions are a beneficial tool for turning 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 turn .7854 radians into degrees, your proportion would be:

π radians.7854 radians = 180 degreesz degrees

To find out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.

This formula implied both ways. Let’s double-check our work by reverting 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.

Now that we've converted one type, it will always work with another unsophisticated calculation. In this instance, after changing .785 from its original form back again, ensuing these steps made perfectly what was predicted -45°.

The formulas work out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Changing Radians to Degrees

Let's go through a handful of examples, so these ideas become simpler to digest.

At the moment, we will change pi/12 rad into degrees. Just the same as before, we will put this number 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 usually would:

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

There you have it! pi/12 radians equals 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

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

Now, what to do if you are required to convert degrees to radians?

By utilizing the very exact formula, you can do the opposite in a pinch by solving for radians as the unknown.

For example, if you wish 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 remember 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 some of the 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 need to make a conversion between radians and degrees.

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