Amplitude, frequency and phase are three parameters of simple harmonic vibration. The period of phase angle is 2π. The initial phase angle of any simple harmonic vibration must be unique in the interval (-π,π］. This uniqueness is often overlooked. When the phase angle is expressed in the form of an arctangent function, the value range of the inverse trigonometric function needs to be considered. The common mistakes in some monographs are corrected here.