What is the domain and range of #y =arccos(sin(2x))#?

1 Answer
Nov 29, 2016

Answer:

The domain is #RR# and the range is #[0,pi]#

Explanation:

The domain of the function #arccos y# is the interval #[-1,1]#.

As #-1<=sin(2x) <=1 AA x in RR#

The function #arccos(sin(2x))# is defined for every #x#.

Besides, #sin(2x)# assumes every possible value in the domain of #arccos y# so the range of the function is the same as the natural range of #arccos#, that is the interval #[0,pi]#.