How Do You Spell VERSED SINE?

Pronunciation: [vˈɜːsd sˈa͡ɪn] (IPA)

The word "versed sine" is often used in trigonometry to describe the distance between the x-axis and a point on a unit circle after the point has rotated a certain angle. The spelling of "versed sine" can be explained using the IPA phonetic transcription as /vɜrst saɪn/. The first syllable "verst" is pronounced with the vowel sound in "herd". The second syllable "sine" is pronounced with the same vowel sound as the word "eye" and the consonant sound in "nose".

VERSED SINE Meaning and Definition

1. The term "versed sine" refers to a mathematical function commonly used in trigonometry and geometry. It is derived from the traditional sine function, but with a distinct interpretation.

   In trigonometry, the sine function typically represents the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. However, the versed sine introduces a different perspective; it represents the ratio of the distance between the vertex of an arc and the midpoint of the chord formed by the arc to the radius of the arc. This definition is particularly relevant when dealing with circular arcs and circles in geometry.

   Mathematically, the versed sine is calculated by subtracting the cosine of an angle from 1. It can also be expressed as the square of the sine of half the angle. Symbolically, the versed sine of an angle θ is denoted as verse(θ) or versin(θ).

   The concept of versed sine finds applications in various fields, particularly in physics and engineering. It is used, for instance, in calculations involving circular motion, arcs of pendulums, and the bending of beams or structures.

   In summary, the versed sine is a trigonometric function that quantifies the displacement between the midpoint of a chord on a circular arc and the vertex of the arc, relative to the radius. Its calculation involves subtracting the cosine of an angle from 1, and it has numerous practical applications in geometry, physics, and engineering.

2. In trig., that part of the diameter intercepted between the sine and the commencement of the arc.

   Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.

Common Misspellings for VERSED SINE

• cersed sine
• bersed sine
• gersed sine
• fersed sine
• vwrsed sine
• vsrsed sine
• vdrsed sine
• vrrsed sine
• v4rsed sine
• v3rsed sine
• veesed sine
• vedsed sine
• vefsed sine
• vetsed sine
• ve5sed sine
• ve4sed sine
• veraed sine
• verzed sine
• verxed sine
• verded sine

Etymology of VERSED SINE

The term "versed sine" is derived from the Latin word "versus", which means "turned or directed towards". In mathematics, the term "sine" refers to the trigonometric function that relates the ratio between the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse.

The term "versed sine" or "versine" was introduced by the Indian mathematician and astronomer Aryabhata around the 6th century. He used the Sanskrit word "jya" to describe a segment of the vertical diameter of a circle intercepted between the sine function and the circumference. When this term was translated into Arabic, it was referred to as "jiba". Eventually, when these mathematical concepts were transferred to Europe, the Arabic "jiba" became "jiva" and then "versa jiva", which evolved into the modern term "versed sine".