October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very crucial ability for higher arithmetic learners to comprehend.

Initially, we need to explain what radians are so that you can perceive how this theorem works in practice. Then we’ll take this a step further by showing a few examples of changing 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 critical theory in geometry and mathematics.

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

Simply put, radians and degrees are merely two separate units of measure used for measuring the identical thing: angles.

Note: a radian is not to be confused with a radius. They are two absolety different things. A radius is the length from the middle of a circle to the perimeter, whereas a radian is a unit of measure for angles.

Relationship Between Radian and Degrees

We have two ways to think regarding this question. The initial way is to think about how many radians there are in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). Therefore, we can state:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The next way to figure out about this question is to consider how many degrees exists in a radian. We understand that there are 360 degrees in a full circle, and we also understand that there are two pi radians in a complete circle.

If we divide each side by π radians, we’ll get 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 upon which you're trying to do.

How to Go From Radians to Degrees?

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

The Formula for Converting Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

Just put in your known values to get your unknown values. For instance, if you wanted to change .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 double-check 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.

Now that we've transformed one type, it will always work with another simple calculation. In this instance, after converting .785 from its first form back again, after these steps made perfectly what was expected -45°.

The formulas solves like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Converting Radians to Degrees

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

At the moment, we will transform pi/12 rad to degrees. Much like before, we will plug this number into the radians slot of the formula and solve 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 it! pi/12 radians equivalents 15 degrees.

Let's try another general conversion and transform 1.047 rad to degrees. Yet 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 precise).

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

By using 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, put in the knowns and solve for 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 handful of examples of how to transform radians to degrees and the other way around. Remember the formula and try it out for yourself the next time you are required to make a conversion from or to radians and degrees.

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