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Yes. The cosine function is continuous. The sine function is also continuous. The tangent function, however, is not continuous.
The function of tang is to fit in the chuck.
The sign function is used to represent the absolute value of a number when used in trigonometry. It is also referred to as the signum function in math.
The functions are periodic and so, given any value (within the range) the function can take the value several times, Graphing the function can help you determine secondary points at which the function takes a given value.
If, at any time, a vertical line intersects the graph of a relationship (or mapping) more than once, the relationship is not a function. (It is a one-to-many mapping and so cannot be a function.)