You should KNOW

1. That since the trig functions are not 1-1 we must

restrict their domains to define their inverses.

2. That the inverse sin of x is the number between -pi/2

and pi/2 whose sin is x, that the domain of the inverse

sin function is [-1,1] (since a number must be in the

interval [-1,1] for it to be the sin of anything), and the

range of the inverse sin is then [-pi/2,pi/2] by definition.

3. That the inverse cos of x is the number between 0

and pi whose cos is x, that the domain of the inverse

cos function is [-1,1] (since a number must be in the

interval [-1,1] for it to be the cos of anything), and the

range of the inverse sin is then [0,pi] by definition.

4. That the inverse tan of x is the number between -pi/2

and pi/2 whose tan is x, that the domain of the inverse

tan function is (-infinity,infinity) (since any number can be

the tan of something), and the range of the inverse tan is then (-pi/2,pi/2) by definition.

5. (You don't need to know the other inverse trig functions.)

6. What the graphs of the inverse sin, cos, and tan look like,

without using your calculator, and how these are related to

the graphs of the sin, cos and tan functions.

7. How to find the values of the inverse trig functions exactly

in the special cases related to the common angles, how to

use degrees and radians appropriately in connection with

the inverse functions, how to find values of the inverse

functions using your calculator.

8. That e.g. sin(arcsin x) = x is always true, but not

arcsin(sin x) = x. (Analogous facts for cos and tan.)

9. How to simplify expressions like cos(arcsin(x)), sin(arctan x).

You should be ABLE TO

1. Give the definitions of the inverse sin, cos, tan; state their

domains and ranges, and sketch their graphs.

2. Find the values of the inverse trig functions exactly

in the special cases related to the common angles,

using degrees and radians appropriately; find values of

the inverse functions using your calculator.

3. Use the inverse trig functions in simple applications.

4. Simplify expressions like cos(arcsin(x)).