This paper proposes a new approach for wide angle monitoring of vital signs in smart home applications. The person is tracked using an indoor radar. Upon detecting the person to be static, the radar automatically focuses its beam on that location, and subsequently breathing and heart rates are extracted from the reflected signals using continuous wavelet transform (CWT) analysis. In this way, leveraging the radar's on-chip processor enables real-time monitoring of vital signs across varying angles. In our experiment, we employ a commercial multi-input multi-output (MIMO) millimeter-wave FMCW radar to monitor vital signs within a range of 1.15 to 2.3 m and an angular span of -44.8 to +44.8 deg. In the Bland-Altman plot, the measured results indicate the average difference of -1.5 and 0.06 beats per minute (BPM) relative to the reference for heart rate and breathing rate, respectively.