Which of the following inverse functions are defined for x=-1/2? select all thst apply. y=cos ^-1x y= cot^-1x y=csc^-1x y=sec^-1x y=sin^-1x y=tan ^-1x

Solution:

Function      Domain

sin−1(x)            [−1,1]   →→→→→Defined

cos−1(x)           [−1,1]  →→→→→Defined

tan−1(x)          (−∞,∞)  →→→→→Defined

cot−1(x)          (−∞,∞)  →→→→→Defined

sec−1(x)        (−∞,−1]∪[1,∞)  →→→→→ not Defined

cosec−1(x)     (−∞,−1]∪[1,∞)  →→→→→not Defined

As, you can see that, all inverse trigonometric functions are defined for, , except sec−1(x)   and cosec−1(x)

, whose domain is not valid or do not exist when , .