Why do the graphs (or the functions themselves for that matter) of arc tan and arc cot follow the graphs of arc sin and arc cos respectively? The trends are, for example the points at which the graphs cross the y-axis, or the directions in which the graphs emerge from the X-axis. Even their principle domains are the same.
Like, cot and tan functions comprise of both sin and cos each, however their inverses seem to follow the trends of the inverses of their numerators respectively. What could be the reasons for this is my question.