1. The inverse of a function f (x), if it exists, is
denoted f^{ -1}(x). The range of f^{ -1}(x) is equal to the

domain of f (x). However, the domain of sin x is “all real numbers,” but the
range of sin^{-1} x is .

Why is this?

It might help to answer the following question first: Why is
not the inverse of g (x) = x^{2}?

Also, has an inverse: what would f^{ -1}(x) be?

2. Let c be some constant. The numbers sin^{-1}(c), cos^{-1}(c), and tan^{-1}(c) are best
described as

(a) areas.

(b) angles.

(c) x-coordinates.

(d) y-coordinates.

3. Let c be some constant. The number sin(c) is best
described as

(a) an area.

(b) an angle.

(c) an x-coordinate.

(d) a y-coordinate.

4. Let c be some constant. The number cos(c) is best described as

(a) an area.

(b) an angle.

(c) an x-coordinate.

(d) a y-coordinate.

5. Use the calibrated unit circle below to approximate the following. If the answer does not exist, say so.

Evaluate the following:

(h) , where A and B are positive numbers.

(i)

(j) , where

(k) , where