Question

True or False. Explain your answer.
csc^-1[csc(-pi/4)]=-pi/4
sec[sec^-1(sqrt3)]=sqrt3

Answer 1

yes

Answer 2

csc^-1 cancels with csc result pi/4
so for sec it cancels with sec^-1

Answer 3

both are inverse of one another if g is inverse of k then
g(k(4))=4

Answer 4

you can also use your calculator to check

Answer 5

Careful, here. While these two are true enough, it is not generally so. With a periodic function, there are Domain issues with the inverse FUNCTION.

For example:

\(csc^{-1}(csc(2\pi/3)) = \pi/3\)

Answer 6

well my friend your right but i think that they are true you can check their domain for confirmation

Answer 7

ya the domains of sec and csc can be greater than 1 or leesss then -1

Answer 8

hows your example true the one you typed now

Answer 9

The RANGE of the inverse cosine function is normally \([0,\pi]\). Anything that starts outside this range may not act as expected.

The RANGE of the inverse sine function is normally \([-\pi/2,\pi/2]\). Anything that starts outside this range may not act as expected.

You can define some other RANGE for these functions, of course, but these are the ones your calculator probably assumes. Therefore ANY ANGLE that is not in this range will map to this range when suffering both functions.