Trig function names: math history?

[EnumaElish]

Does anyone know how the function names sin, cos, csc, sec, ... came about?

Wouldn't they be easier to remember if cos was 1/sin; csc was 1/sec; just like cot is 1/tan? (Instead of 1/sin = csc and 1/cos = sec.)

This is one thing in trig that always throws me off.

 

[TenaliRaman]

Probably a read of this link would help you appreciate the usage of these words,
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Trigonometric_functions.html

Note that these notations came out of necessity (for simplification) and not through a magic wand

-- AI

 

[Galileo]

Bah. Here we just learn sin, cos and tan. Period.
Why use extra terms (csc, sec cot) for 1/sin etc. You hardly encounter them anywhere anyway. Trig is complicated enough with all the relations among sin, cos and tan. It's only making it more complicated.

 

[HallsofIvy]

The "co" is from the fact that the cosine is the sine of the complementary angle (90 degrees minus θ- the other angle in the right triangle). Same for cotangent, cosecant. Perfectly reasonable.