radian
/'reidjən/
Definition
- Noun:
- A unit of angular measurement: The radian is the standard unit of plane angle in the International System of Units (SI). It is defined by the geometry of a circle: one radian is the angle created when the length of the arc on the circle's circumference is exactly equal to the length of the circle's radius.
Usage
- The radian is a dimensionless unit used extensively in mathematics, physics, and engineering, particularly in calculus and trigonometry, because it simplifies many formulas.
- It is the preferred unit for angular measurement in advanced mathematics, as opposed to degrees.
Examples
- Noun:
- A full circle contains 2π radians.
- The angle θ is measured in radians.
- Convert 90 degrees to radians; the result is π/2 radians.
Advanced Usage
- "In terms of radians": Expressing an angle using the radian unit.
- The sine function has a simple derivative when the angle is in terms of radians.
- "Radian measure": The measurement of an angle in radians.
- We will solve this trigonometric equation using radian measure.
Variants and Related Words
- Steradian (n): The SI unit of solid angle, analogous to the radian for three-dimensional angles. It is the three-dimensional equivalent.
- Luminous intensity is measured in candelas per steradian.
Synonyms
- SI angular unit: The standard unit for angle in the International System.
- Circular measure: A term sometimes used to describe angular measurement based on the arc of a circle, of which the radian is the primary example.
Related Phrases and Concepts
- Arc length: The distance along the curved line of a circle's circumference. The radian is defined by the relationship: arc length = radius × angle (in radians).
- Unit circle: A circle with a radius of 1. On the unit circle, the angle in radians is numerically equal to the length of the arc it subtends.
Noun
-
the unit of plane angle adopted under the Systeme International d'Unites; equal to the angle at the center of a circle subtended by an arc equal in length to the radius (approximately 57.295 degrees)
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