sine

/sain/

Thân thiện

A student calculates the sine of an angle on a geometry worksheet.

Definition

1. Noun:
   • A trigonometric function: In a right-angled triangle, the sine of an acute angle is the ratio of the length of the side opposite that angle to the length of the hypotenuse.

Usage

• The word sine is primarily used as a mathematical term. It is often abbreviated as sin in formulas and calculations.
• It is used to relate angles to side ratios in right triangles and is fundamental in trigonometry, calculus, and many applied sciences like physics and engineering.

Examples

• Noun:
  • The sine of a 30° angle is 0.5.
  • To find the height of the building, we calculated the sine of the elevation angle.
  • In the equation sin(θ) = opposite / hypotenuse, sin represents the sine function.

Advanced Usage

• Sine wave: A smooth, periodic oscillation described by the sine function, commonly used to represent sound waves, light waves, and alternating current.
  • The pure tone produced by the tuning fork is a perfect sine wave.
• Law of Sines: A theorem in trigonometry stating that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles.
  • We used the Law of Sines to solve the triangle because we knew two angles and one side.

Variants and Related Words

• Sin (abbreviation): The standard abbreviation for sine in mathematical notation.
  • The graph plots y = sin(x).
• Sine curve: Another term for a sine wave, the graphical representation of the sine function.
• Arcsine (noun): The inverse function of the sine, written as or . It returns the angle whose sine is a given number.
  • If sin(θ) = 0.707, then θ = arcsin(0.707) is approximately 45°.

Synonyms

• Trigonometric ratio: A more general term for functions like sine, cosine, and tangent.

Related Phrases and Idioms

• Sine qua non (Latin phrase adopted into English): An essential condition; a thing that is absolutely necessary. While it contains the word "sine," its meaning is unrelated to the mathematical term.
  • Trust is a sine qua non for a successful partnership.

Học thuật

Noun

1. ratio of the length of the side opposite the given angle to the length of the hypotenuse of a right-angled triangle

Từ đồng nghĩa

• sin