Posted by Anonymous on Monday, May 25, 2009 at 12:08pm.
Determine whether each equation is true for all x for which both sides of the equation are defined. If it is true, support your conclusion with a sketch using the unit circle. If it is false, give a counterexample.
inverse sin(x)=inverse sin(x)
inverse cos(x)=inverse cos(x)
I think that the first one is true and the second one is false but I do not know what to put down as a sketch or counterexample. Any help is appreciated.

Math  PC, Monday, May 25, 2009 at 12:36pm
The simplest way to determine if
inverse f(x) =inverse f(x)
is true for all values of x is to find out if f(x)=f(x) for all values of x.
Substitute sin(x) or cos(x) for f(x) above and do a little sketching of each of the two trigonometric functions between pi and +pi. You will get your answer by simply looking at the sketches.