Question

True or False:
arc csc[csc(-π/4)]= -π/4

Answer 1

According to definition of inverse function i would say True

Answer 2

or is this a trick question...hold on

Answer 3

cscx=1/sinx
the domain of cscx is (-pi/2,pi/2) since we also want to make cscx 1 to 1

Answer 4

so the range of arc csc wouldn't include -pi/4

Answer 5

so false

Answer 6

or did i miss something

Answer 7

yep, good catch...its false

Answer 8

i think it may be true

Answer 9

i cant think anymore tonight
goodnight

Answer 10

wolfram and maple say it is true

Answer 11

i think the domain of cscx is (-pi,pi)

Answer 12

that is where i went wrong

Answer 13

well from an equation standpoint, if you take csc of both sides you show equality.
the domain can't have zero in it though

Answer 14

domain of arc csc is [-1,1]
csc (-pi/4) = -sqrt(2)
so it would be False

Answer 15

like i said...trick question
mathematically you can't compute left side but you can show equality using inverse function property