October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very essential skill for progressive math learners to comprehend.

First, we are required to explain what radians are thereby you can see how this formula works in practice. Then we’ll take it one step further by exhibiting some examples of converting from radians to degrees easily !

What Is a Radian?

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

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

That being said, 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 completely different things. A radius is the distance from the center of a circle to the edge, though a radian is a unit of measure for angles.

Correlation Between Radian and Degrees

We have two manners to go about regarding this question. The initial method is to contemplate about how many radians there are in a full circle. A full circle is equal to 360 degrees or two pi radians (precisely). Therefore, we can say:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The next way to figure out regarding this question is to consider how many degrees there are 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 whole 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 depending on what you're trying to get.

How to Convert Radians to Degrees?

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

The Formula for Converting Radians to Degrees

Proportions are a beneficial tool for converting a radian value into degrees.

π radiansx radians = 180 degreesy degrees

Just put in your known values to derive your unknown values. For instance, if you wished to convert .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 can be implemented both ways. Let’s recheck our workings by converting 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.

Now that we've converted one type, it will always work with another straightforward calculation. In this case, afterwards converting .785 from its first form back again, ensuing these steps created precisely what was anticipated -45°.

The formulas plays out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Converting Radians to Degrees

Let's try some examples, so these concepts become easier to digest.

Now, we will convert pi/12 rad to degrees. Just like before, 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 normally would:

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

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

Let's try one more general conversion and transform 1.047 rad to degrees. One more time, utilize the formula to get started:

Degrees = (180 * 1.047) / π

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

Right away, what happens if you have to convert degrees to radians?

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

For example, if you have to change 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 memorized the equation to find radians, you will get identical answer:

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. Bear in mind the equation and try solving for yourself the next time you need to make a change from or to radians and degrees.

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