radian

/'reidjən/

Thân thiện

A teacher draws a radian on the chalkboard.

Definition

1. 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.

Học thuật

Noun

1. 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)

Từ đồng nghĩa

• rad