Inverse Trigonometric Functions,

Can you please help me solve this exersise ? http://screencast.com/t/l72oUq8pXdX

Question

Inverse Trigonometric Functions,

Can you please help me solve this exersise ? http://screencast.com/t/l72oUq8pXdX

hero · Answer

#veryeasy

christos · Answer

:/

hartnn · Answer

http://en.wikipedia.org/wiki/Inverse_trigonometric_functions see the 2nd table

hartnn · Answer

under 
'Relationships between trigonometric functions and inverse trigonometric function'

hero · Answer

Okay, so for the first one:

$\sin^{-1}\left(\sin\left(\dfrac{\pi}{7}\right)\right) = \dfrac{\pi}{7}$  because inverse trig functions cancel leaving only the argument.

christos · Answer

so (b) is 5pi/7 ? @hero @hartnn

hartnn · Answer

yes

christos · Answer

Ok so these are all "true" ? http://screencast.com/t/AnZGifYWi

christos · Answer

except zero for tans  *

christos · Answer

or maybe not , idk -_-

hartnn · Answer

all are always true , even for 0's
tan (arc tan0) = 0 
arctan (tan 0) =0

christos · Answer

I see ! ty

christos · Answer

The solution manual is harder than I expected -_- http://screencast.com/t/8jOtQ4Ipd @hartnn @Hero Maybe is saying the same thing in different way or is there any slight difference ?

hartnn · Answer

what is different ? just their domains are mentioned...

christos · Answer

aah -_-

hartnn · Answer

look at the domains of various inverse trigo functions from wiki