When measuring angles, you can choose between using radians or degrees. Both units have their own advantages and disadvantages, so it’s important to know when to use each one.
Radians
Radians are a unit of angular measure that is based on the circumference of a circle. One radian is defined as the angle that is subtended by an arc of a circle that has a length equal to the radius of the circle.
Radians are often used in mathematics and physics because they are a more natural unit of measure for angles than degrees. For example, the radian measure of a full circle is 2π, which is a much more elegant expression than the degree measure of 360°.
Degrees
Degrees are a unit of angular measure that is based on the division of a circle into 360 equal parts. One degree is defined as 1/360 of a full circle.
Degrees are often used in everyday life because they are a more familiar unit of measure than radians. For example, we measure the angles of triangles in degrees, and we use degrees to indicate the direction of the wind.
When to Use Radians
Radians are the preferred unit of measure for angles in mathematics and physics. This is because radians are a more natural unit of measure for angles than degrees. For example, the radian measure of a full circle is 2π, which is a much more elegant expression than the degree measure of 360°.
Radians are also used in many applications in engineering and science. For example, radians are used to measure the angles of rotation in machines, and they are used to calculate the trajectory of projectiles.
When to Use Degrees
Degrees are the preferred unit of measure for angles in everyday life. This is because degrees are a more familiar unit of measure than radians. For example, we measure the angles of triangles in degrees, and we use degrees to indicate the direction of the wind.
Degrees are also used in many applications in navigation and surveying. For example, degrees are used to measure the latitude and longitude of locations on the Earth.
Table of When to Use Radians or Degrees
| Application | Radians | Degrees |
|---|---|---|
| Mathematics | Yes | No |
| Physics | Yes | No |
| Engineering | Yes | Sometimes |
| Science | Yes | Sometimes |
| Everyday life | No | Yes |
| Navigation | No | Yes |
| Surveying | No | Yes |
Conclusion
Radians and degrees are both valid units of angular measure. However, radians are the preferred unit of measure for angles in mathematics and physics, while degrees are the preferred unit of measure for angles in everyday life.
