Definition

1. Noun:
   • A branch of trigonometry: Spherical trigonometry is the specific area of mathematics that deals with the relationships between the sides and angles of triangles drawn on the surface of a sphere.

Usage

• Spherical trigonometry is essential for calculations in astronomy, geodesy, and navigation, where positions and distances on a spherical surface like the Earth or celestial sphere must be determined.
• The formulas in spherical trigonometry differ from those in plane trigonometry due to the curved surface.

Examples

• Noun:
  • Astronomers use spherical trigonometry to calculate the positions of stars and planets.
  • Solving problems in great-circle navigation requires a solid understanding of spherical trigonometry.

Advanced Usage

• "the laws of spherical trigonometry": Refers to the fundamental theorems and formulas, such as the law of sines and the law of cosines for spherical triangles.
  • The navigator applied the laws of spherical trigonometry to plot the most efficient course across the ocean.

Variants and Related Words

• Spherical triangle (n): A triangle formed by three arcs of great circles on the surface of a sphere, which is the primary subject of study in spherical trigonometry.
  • A spherical triangle has angles whose sum is greater than 180 degrees.
• Spherical geometry (n): The broader branch of geometry that studies figures on the surface of a sphere, which encompasses spherical trigonometry.
  • The study of spherical geometry becomes important when considering large-scale distances on Earth.

Synonyms

• None commonly used: It is a precise, technical term for a specific mathematical field. Related general terms include trigonometry on a sphere or the trigonometry of spherical triangles.

Related Phrases

• "to apply spherical trigonometry": To use its principles and formulas to solve a problem.
  • To find the shortest flight path, the pilot had to apply spherical trigonometry.

Related Idioms

• None: This is a specialized academic term and is not used in idiomatic expressions.

Noun

1. (mathematics) the trigonometry of spherical triangles