The functions tangent, cotangent, secant, and cosecant have asymptotes where the denominator vanishes. These points are essential discontinuities. The functions are continuous at all other points.
As discussed in conjunction with power functions, arcsine and arccosine are not continuous at the endpoints -1 and 1 because only the right-hand limit exists at -1 and only the left-hand limit exists at 1. However, both arcsine and arccosine are right-continuous at x=-1 and left-continuous at x=1.
The functions arcsec(x) and arccos(x) are defined for
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CalculusQuest^{TM}
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All rights reserved---1996
William A. Bogley
Robby Robson