Exercises for Chapter III Section 2

Do NOT use a calculator for any of these problems, give only exact answers. (See Preface)

1. What might be the motivation for choosing the interval as the domain of the Cosine function?

2. Give the domain and range of: (a) Arctan(x); (b) Arccos(x).

3. Find Arcsin(½) and four other real numbers x such that sin(x) = ½.

4. Find and four other real numbers x such that

5. Find: (a) Arcsin(1);      (b) Arctan(1);      (c) Arccos(½).

6. Find: (a)       (b)       (c) Arccos(-1).

7. (a) Graph both y = Cos(x) and y = Arccos(x) on the same axes.

    (b) Are these graphs symmetric to each other with respect to some line?

8. Graph; (a) y = Arcsin(x);      (b) y = Arctan(x).