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Radians to Degrees

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To measure the angles in geometry, we have two different measuring systems. The units that we use to measure the angles are radians and degrees. We can convert the measures from radians to degrees by using a formula. In this blog, we’ll understand the conversion of radians to degrees in a detailed way.

Degrees to Radians Conversion

The conversion of an angle from degrees to radians is just the opposite of what we would learn about radians to degrees. The conversion from degrees to radians can be done using a simple derived formula and that is Angle in radians= angle in degrees×π/180°.

Radians to Degrees Conversion

We have two individual units to measure the angles and those are radians and degrees. Therefore, we need to understand well the conversion of angle units, radians to degrees, and degrees to radians. We’ll dive into the details of what each of the units means in this blog.

Radians

If we rotate the radius that we take out of a circle, completely around it, it makes one rotation. After one complete rotation, the radius makes an angle at the center and the value of the angle is 2π radians. The angle which is made at the center of the circle is equal to the ratio of the length of the arc and the length of the radius of the circle. If the length of the arc and the length of the radius become the same, then the angle subtended at the center of the circle is equal to 1 radian. The SI unit of measuring angles is radians.

Degrees

One single revolution is divided into 360 equal parts, every part is named as a degree. The angle created at the center of the circle, after one complete rotation of the radius is 360°. The symbol that is used to express degrees is ‘°’. Although degrees is not the SI unit for measuring angles, it is accepted as a unit to measure. In most cases, the unit of the angle is converted from radians to degrees for our convenience.

360 degrees=2π radians

180 degrees=π radians

Formula of Radians to Degrees Conversion

The formula of radians to degrees is used to convert the value from radians to degrees. To convert into the later one, we have to multiply radians by 180°/π radians. When the value is in degrees, we write it as 1°, whereas, in the case of radians, we write it as 1, or, 1c. A complete rotation around the circle is 2π in radians and 360° in degrees. The required formula of conversion of an angle from radians to degrees-

Angle in radians×180°/π = Angle in degrees

How to Convert Radians to Degrees

As we have discussed earlier, radians and degrees are two individual units to measure angles. After one complete revolution of a circle, we can conclude that 2πradians= 360°. An angle that is given in radians can be converted into degrees by following the given steps:

● You should note down the measure of the angle which is given in radians.

● Given that 1 radian=180°/π, to convert the angle to degrees multiply the value with 180°/π.

● Simplify and express the value in degrees (°).

Let us look into an example.

Example: The value of the angle mentioned is π/6 radians. Convert the value into degrees by using the conversion formula.

Solution: (π/6) ×180°/π= angle in degrees

Therefore, the angle in degrees=30°.

Some of the Important Notes on Radians to Degrees Conversion

● We measure angles using two units and those are radians and degrees.

● A full counterclockwise revolution of a circle is equal to 2π radians.

● 1 radian is equal to 57.2958° and 1° is equal to 0.017453 radians.

● If we need to convert an angle from degrees to radians, we have to multiply the value with π/180°.

● If we need to convert the angle from radians to degrees, we multiply it by 180°/π.

To learn more about Radians to Degrees and Degrees to Radians conversion, visit the Cuemath website for all math-related questions. 

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