Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: e Inverse Trigonometric Functions As the title indicates, in this section we concern ourselves with ﬁnding inverses of the (circular) trigonometric functions. Our immediate problem is that, owing to their periodic nature, none of the six circular functions is one-to-one. To remedy this, we restrict the domains of the circular functions in the same way we restricted the domain of the quadratic function in Example 5.2.3 in Section 5.2 to obtain a one-to-one function. We ﬁrst consider f (x) = cos(x). Choosing the interval [0, π ] allows us to keep the range as [−1, 1] as well as the properties of being smooth and continuous. y x Restricting the domain of f (x) = cos(x) to [0, π ]. Recall from Section 5.2 that the inverse of a function f is typically denoted f −1 . For this reason, some textbooks use the notation f −1 (x) = cos−1 (x) for the inverse of f (x) = cos(x). The obvious pitfall here is our convention of writing (cos(x))2 as cos2 (x), (cos(x))3 as cos3 (x) and so on. It 1 is far too easy to confuse cos−1 (x) with cos(x) = sec(x) so we will not use this notati...
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