Calculus inverse trig question

Question

arccos(cos 7π/5)=?

the answer is 3π/5 but I do not understand how to get it.

why does 4π/5 not work since it is also in the (0,π) range

thankyou for the help!

Answer 1

Remember:

Cos (2π-x)= Cos (x)

 

Arccos(cos(x))= x + 2kπ, when k∈Z (k is integer).

 

wrt to the properties above:

 

arccos(cos 7π/5)=arccos(cos(2π - 3π/5)) = arccos(cos(3π/5))= 3π/5.