In this paper, we propose a fault diagnosis method based on Park's Vector Approach using the Euler's theorem. If we interpreted it as Euler's theorem, it is possible to easily find the phase angle difference between the healthy condition and the fault condition. And, we analyzed the variation of the phase angle and performed the diagnostic method of the induction motor using feature vectors that were obtained by using a Fourier transform. The analysis of time and speed variation of the motor was performed and, as a result, we could find more soft variations than rough variations. In particular, the analysis of the distortion through each phase shows that two-turn and four-turn shorted motors are linearly separable. In this experiment, we know that the maximum breakdown threshold value for determining steady-state fault detection is 49.0788. Simulation and experimental results show the more detectable than conventional method.