Question: 3. As you know the function cos is not one-to-one. Let k 2 Z. (a) Find the largest interval Ik such that k + 1

3. As you know the function cos is not one-to-one. Let k 2 Z. (a) Find the largest interval Ik such that k + 1 2 Ik and the restriction of cos to Ik is one-to-one. (b) We will call k the inverse function of the restriction of cos to Ik . What are the domain and the range of k ? Sketch its graph. (Make sure to label the axes appropriately.) (c) For which values of t 2 R and s 2 R are the following equations true? cos(k (t)) = t k (cos(s)) = s (1) (d) Compute k (cos(2017)) and cos(k (2017)). (e) Beginning with Equation (1), take derivatives of both sides with respect to t to obtain an explicit formula for k0 . 1 Hint: The answer is not k0 (x) = p . 1 x2

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