Radians to Degrees

About Radians to Degrees

Radians to degrees is a type of conversion used in geometry to convert angle measurements. There are two alternative methods for measuring an angle. Radians and degrees are the two units used to measure angles. The radian unit is most commonly used in trigonometry. A formula can be used to convert radians to degrees when measuring angles. To comprehend this formula and convert radians to degrees, we must first comprehend the definition of each angle unit.

Radians to Degrees Conversion

Angles are measured using two separate units: radians and degrees. As a result, we must be adept in the conversion of angle units, such as radians to degrees and degrees to radians. We begin to construct an angle that may be measured in radians or degrees when we take the radius of a circle and revolve it.

Radians

One rotation is completed when the radius is rotated completely around the circle. After one complete rotation, the radius subtends a 2 radian angle at the circle's centre. The ratio of the length of the arc to the length of the radius is the angle in radians subtended by the radius at the centre of the circle. The angle subtended at the centre becomes 1 radian when the length of the arc equals the length of the radius. The radian unit is abbreviated as rad. The SI unit for measuring angles is radians.

Degrees

Degrees are used to measure angles. A revolution is divided into 360 equal pieces, each of which is referred to as a degree. After one complete rotation of the radius, the angle subtended in the centre of the circle is 360°. The letter '°' is used to represent degrees. Although degrees are not a SI unit for measuring angles, they are a widely used measurement unit. As a result, it is preferable to convert the unit of angle from radians to degrees while solving problems to better grasp it. A protractor is a tool that is used to measure angles in degrees.

When we compare the angle measurements for a complete revolution, we find that

360 Degrees = 2π Radians

180 Degrees = π Radians

Radians to Degrees Formula

To convert radians to degrees, use radians to degrees formula. We can convert radians to degrees by multiplying them by 180°/radians. We use two sorts of units to measure angles: degrees and radians. A degree is expressed as 1°. And 1 radian is expressed as 1 (or) 1c, which signifies that if there is no unit following the angle measurement, it is in radians. A circle's rotation is divided into 360 equal pieces, each of which is referred to as a degree. In radians, a complete counterclockwise revolution is 2; in degrees, it is 360°. As a result, the degree and radian measurements are linked. To convert an angle in radians to degrees, use the following formula:

Angle in Radians × 180°/π = Angle in Degrees

Degree(°)	Raddian(rad)
0°	0
30°	π/6
45°	π/4
60°	π/3
90°	π/2
120°	(2π)/3
135°	(3π)/4
150°	(5π)/6
180°	π
270°	(3π)/2
360°	2π

Radians to Degrees

About Radians to Degrees