The cosine function, like all of the trigonometric functions, is periodic about the rotation around a circle. Since the cosine is defined as the adjacent/hypotenuse of a right triangle, you can clearly see that its value can never be greater than one or less than -1 since the hypotenuse is always longer than the adjacent side. It turns out that, indeed, the cosine's range is from -1 to 1, written [-1,1].
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The inverse of the cosine is the secant.
The range of a function is the interval (or intervals) over which the independent variable is valid, i.e. results in a valid value of the function.
The range is infinite in both directions.