Everyone knows the difference between a necessary condition and a sufficient condition, but in the heat of battle the distinction between them can be forgotten. The distinction can obtain also at the meta level. A nice example is being asked to ascertain whether the cotangent of 40 degrees is greater than the cosine of 5 degrees. It would be sufficient is we knew the two values, because we could then just inspect them and draw the appropriate conclusion, but it is not necessary. It is sufficient merely to note that the cotangent of 40 degrees must be greater than 1, and that the cosine of 5 degrees must be less than 1 to conclude that, indeed, the cotangent of 40 degrees is greater than the cosine of 5 degrees.

keywords: Mathematics, Logic, Trigonometry, trigonometric functions

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