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)).