### Trigonometric Functions

The functions cosine and sine are defined for all real numbers and are continuous for all real numbers.

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.

The inverse trigonometric functions arctangent and arccotangent are defined for all real numbers and are continuous. The functions arcsine and arccosine are defined on the interval [-1,1] and are continuous on the open interval (-1,1). (This means they are continuous at every point of this open interval).

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 x -1 and x 1. They are continuous for x < -1 and x >1 and are only right- and left-continuous at the endpoints -1 and 1.

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