please explain the steps to check for the right angle when taking arctan in wave function example: Y(x,y)=Acos(kx+wt+phi), dY/dt= - wAsin(phi) at t=0 x=0, wave travels in negative direction, and transverse speed is traveling downward ( want positive position and a negative velocity?!! which happens when both sin and cos terms are positive?!!)

In another example: X(t)=Acos(wt+phi) if w=2rad/s X(0)= - 0.5m and V(x)(0)= - 1 m/s. The correct angle is phi + pi ( what is the logic/ steps to determine the correct angle in dealing with arctan ? concerning the wave speed and direction ???