Find sin(arccsc(20)), where arccsc(theta) = the inverse of csc(theta)

Question

hartnn · Answer

do you know this property?
$arccsc(x)=arcsin(1/x)$
use this.

hartnn · Answer

@KatClaire  Hi,

$\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile$

did u get what i have written above ?
if not, you can just ask.

anonymous · Answer

Haha sorry I'm trying to piece it all together. My prof didn't go over this so I'm not quite undrestanding the concept of what arc is?

hartnn · Answer

arc here means inverse
if sin x = y
x= arcsin y
read as 'x is sin inverse y'

hartnn · Answer

now since sin x = 1/ csc x
you have property of inverse trignometric function as :
arccsc x = arcsin (1/x)
so what will be 
arccsc(20) = ??
in terms of arcsin ?

anonymous · Answer

Is it 0.05?

anonymous · Answer

[-\left( 1\div \left| x \right|\sqrt{x ^{2}-1} \right)\]$$-\left( 1\div \left| x \right|\sqrt{x ^{2}-1} \right)$$

anonymous · Answer

that being my question... do I just sub in 20? Or am I a moron

hartnn · Answer

i thought the question is sin(arccsc(20)) 
 = sin(arcsin(1/20))
=1/20
=0.05 is correct

hartnn · Answer

why u wanna substitute 20 there ?

anonymous · Answer

oooooh okay I get it now. I was just getting messed up with derivatives. Thanks for your help!