When studying mathematics and physics, we often involve the concepts of angle and radian. Angle is the included angle between an object or two lines, usually expressed in degrees, while radian refers to the angle corresponding to an arc whose arc length is equal to the radius, usually expressed in radian system. In mathematics and physics, arc system is a very important concept, because it can help us better understand and solve problems.

Conversion formula of arc system and angle system

In the radian system, the radian number of a complete circle is 2π, which is 360 degrees. Therefore, we can get the following conversion formula:

1 degree =π/ 180 radians

1 radian = 180/π degrees

How to convert angles into radians

If we want to convert angles into radians, we can follow the following steps:

1. Divide the angle value by 180, and the result is radian value.

2. Multiply the radian value by π to get the final radian value.

For example, if we want to convert 30 degrees into radians, we can follow the following steps:

1.30 degrees÷180 = 0.1667

2.0. 1667×π=0.523 radian

Therefore, 30 degrees is equal to 0.523 radians.

How to convert radians into angles

If we want to convert a radian into an angle, we can follow the following steps:

1. radian value multiplied by 180, the result is the angle value.

2. Divide the obtained angle value by π to get the final angle value.

For example, if we want to convert 1 radian into an angle, we can follow the following steps:

1. 1 radian×180 = 57.296 degrees.

2.57.296÷π= 18.295 degrees.

So 1 radian is equal to 57.296 degrees.