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

Question

dumbcow · Answer

According to definition of inverse function i would say True

dumbcow · Answer

or is this a trick question...hold on

myininaya · Answer

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

myininaya · Answer

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

myininaya · Answer

so false

myininaya · Answer

or did i miss something

dumbcow · Answer

yep, good catch...its false

myininaya · Answer

i think it may be true

myininaya · Answer

i cant think anymore tonight
goodnight

myininaya · Answer

wolfram and maple say it is true

myininaya · Answer

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

myininaya · Answer

that is where i went wrong

dumbcow · Answer

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

dumbcow · Answer

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

dumbcow · Answer

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