Essay - Sine, Cosine, and Tangent When Using Trigonometric Functions, the Three...

Sine, Cosine, and Tangent

When using trigonometric functions, the three sides of a right triangle (opposite, adjacent and hypotenuse) are identified in relation to a chosen angle. The trigonometric functions (sine, cosine, ***** tangent) are then defined in relation ***** the ***** sides of the right triangle.

***** word "s*****e" comes from the Latin word "sinus," which means a bend or gulf, or the bosom of a garment. (Gelfand) The term was used as a translation for ***** Arabic word "jayb," the ***** for a sine that also meant ***** bosom of a garment, and which in turn comes from the Sanskrit word "jiva," which translates to bowstring.

Originally the word "*****" ***** applied to the line segment CD on a figure, which meant it w***** half the chord of t*****ice ***** angle AOB. A sine resembles a ***** in this reg*****rd. ***** ratio of the s*****e CD to the radius of the circle, OA, is the sine of angle AOB.

The word "*****" was originally written like this: "co.*****," which was the abbreviated version of the sine ***** the complement, or "complimenti *****." The cosine of an ***** is ***** sine of the complementary *****gle.

Relationships between the lengths of the sides and the sizes of the angles of a triangle are given by ***** ***** and ***** rules. If there ***** enough in*****mation already, the cosine and sine rules can be used to find the length of a side, ***** the size of an *****gle. Typically, these methods are ***** only for *****s that do not have a ***** angle because easier ***** ***** finding the dimensions of right-*****d triangles exist.

***** word "*****" is taken ***** ***** ***** word "tangens," which is related to the word "tangere," meaning "to *****uch." (Gelfand) The term was ***** ***** to ***** line segment AB in a figure: the segment ***** the t*****ngent ***** the ***** at A th***** is cut off by ***** extension of OB. The ratio of *****e tangent AB to the radius of the circle, OA, is the tangent ***** angle AOB.

History of Sine, ***** and Tangent

As far back as 140 B.C., when Greek mathematician Hipparchus was the first to study triangular geometry, trigonometry has existed. In these early days, trigonometry ***** used for astronomy. (Kay) Hipparchus is considered the founding father of trigonometry because he is said to have written the ***** 12 books on tables of chords.

Over the years, trigonometry ***** advanced. Another Greek mathemetician, Apollonius, was the next ***** contribute to ***** field. Apollonius formulated planet's position, leading ***** *****'s tabulating ratios enabling planet positions.

The next important d*****covery in ***** came from the Islamic people, who also related ***** to trigonometry. (Kaye) ***** ***** Abu Abdallah Muhammad ibn Jabir al-Battani formally introduced *****. The Islamic people also resurfaced the ***** function. ***** cotangent, secant and co***** ***** were introduced and it was later made known that they ***** the reciprocals of tangent, sine, ***** cosine.

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