Trig function names: math history?

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EnumaElish
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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.
 

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Galileo
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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
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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.
 

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