Hi! I need some help with these 2 questions. thank you in advance.

First one

Is not one-to-one

(-pi/2, pi/2)

Second one....Correct  !!!

cos  ( arcsin (-0.845))

Easy way : 

arcsin (-0.845) = - 57.67°

cos (-57.67°)  ≈ .535 

"Expert" way

We are looking for  the cosine  of an angle whose sine =  -845/ 1000 =  y  /r

Remember that cosine  =  x /r

We need  to  find x  

x =  ±√ [ r^2 - y^2]  = ±√ [ 1000^2 - 845^2 ] = ±534.76 = ±535

This angle is in the 4th quadrant  (the sine is negative there).....but  the cosine is positive in this quadrant

So

cosine  for this angle =  x / r  =  535 / 1000   =  .535