Geometric connection to Trig Functions
This figure shows all of the segments that comprise the 6 trigonometric functions.
When the sine was invented in early India, it was called “half-chord”, or “jya-ardha” in Sanskrit. This eventually got shortened to “jya”. When it was translated into Arabic, the Arabic mathematicians transliterated the word to “jayb”. (Every Arabic noun has three consonants, so they stuck a B on the end.) This word had no intended meaning, just a transliteration…but it turned out that "jayb" DID have a meaning. In Arabic, "jayb" is the word for a bay, gulf, or cove… When it got transcribed to Latin, they used this meaning, and the Latin word is “sinus”; the same "sinus" that is used in “sinus cavity” (a bay or gulf inside your skull). The word “sinus” is still used in some eastern European countries, but in most places it’s been abbreviated to “sine”. And then we have the SINE of the COMPLIMENTARY angle, or COsine. Secant is the line that cuts the Tangent line. And Tangent is the line tangent to the circle (perpendicular to the radius). COSecant and COtangent are simply the Secant and Tangent of the Complimentary angle (or of the triangle formed when using the Complimentary Angle). Can you see all of these segments in the figure?