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 , .

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,