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Linguistic Note on Cotangent
Like tangent, the word cotangent comes from the Latin tangentus that which is touching, the present participle of tangere to touch.
The co- prefix, as with similar trigonometric functions, is a reference to complementary angle: see Cotangent of Complement equals Tangent.
It is pronounced with an equal emphasis on both the first and second syllables: co-tan-jent.