evaluate the following composite expressions please provide A sketch of the right triangle related to the inside expression. easily understandable explanation

Question

arctan(tan(5∏/4))

Answer 1

pi/4 or 45 degrees

has the same tangent value but it's in the domain of arctan(x), while 5pi/4 is not

tan(5pi/4)= tan(pi/4) = tan(45)= tan(225)= 1 = tan(pi/4+npi) where n= any integer

but

-pi/2 < arctan(x) < pi/2, by definition or convention

otherwise you're very tempted to say falsely that arctan(tan(5pi/4)= 5pi/4