Using the capability that an optoelectronic oscillator (OEO) can generate microwave signals and modulation polarization sensitivity of Mach-Zehnder modulator (MZM), we design a triangular wave and sinusoidal signal generator which is an OEO system embedded by the triangular waveform generator. The bias of the MZM is set at the minimum transmission point, and the polarization angle of the light beam is controlled so that light enters the MZM with an angle for the best modulation axis. The component of the light field parallel to the best modulation axis is modulated by the optical carrier suppression in MZM to generate the odd-order sidebands, but the orthogonal component keeps unchanged. After filtering the negative sidebands and projecting the light field in the same direction by the analyzer, we generate a triangular waveform signal in the photodetector (PD). When the triangular waveform signal passes an electric bandpass filter, the corresponding sinusoidal microwave signal is obtained, which can also complete oscillation feedback for the OEO system. The principle of triangular waveform generation is theoretically analyzed and simulated. In the experiments, a clear and steady triangular waveform signal with a repetition frequency of 5 GHz is generated, meanwhile the sinusoidal microwave signal can be obtained simultaneously. With only a few devices added in OEO, the proposed scheme can generate both triangular waveform and sinusoidal signal simultaneously, which has the advantages of simple structure and practicability.