An electric power steering apparatus which comprises: an angle detector for outputting a sine wave signal and a cosine wave signal corresponding to a rotor position of a brushless DC motor for assisting steering; a torque detector for detecting a steering torque applied to a steering member; and an abnormality detecting unit for detecting occurrence of abnormality in said angle detector; and which drives said brushless DC motor to assist steering based upon the sine wave signal and the cosine wave signal outputted from said angle detector and the steering torque detected by said torque detector, characterized in that said abnormality detecting unit includes: sine wave signal squaring means for squaring the sine wave signal detected by said angle detector; cosine wave signal squaring means for squaring the cosine wave signal detected by said angle detector; adding means for adding the sine wave signal squared by said sine wave signal squaring means to the cosine wave signal squared by said cosine wave signal squaring means; judging means for judging whether or not the addition result by said adding means falls within a predetermined range; and abnormality detecting means for detecting occurrence of abnormality in said angle detector when said judging means judges that the addition result does not fall within the predetermined range, wherein the upper limit of the predetermined range is determined based upon respective error ranges of the sine wave signal and the cosine wave signal. an angle detector for outputting a sine wave signal and a cosine wave signal corresponding to a rotor position of a brushless DC motor for assisting steering; a torque detector for detecting a steering torque applied to a steering member; and an abnormality detecting unit for detecting occurrence of abnormality in said angle detector; and which drives said brushless DC motor to assist steering based upon the sine wave signal and the cosine wave signal outputted from said angle detector and the steering torque detected by said torque detector, characterized in that said abnormality detecting unit includes: sine wave signal squaring means for squaring the sine wave signal detected by said angle detector; cosine wave signal squaring means for squaring the cosine wave signal detected by said angle detector; adding means for adding the sine wave signal squared by said sine wave signal squaring means to the cosine wave signal squared by said cosine wave signal squaring means; judging means for judging whether or not the addition result by said adding means falls within a predetermined range; and abnormality detecting means for detecting occurrence of abnormality in said angle detector when said judging means judges that the addition result does not fall within the predetermined range, wherein the upper limit of the predetermined range is determined based upon respective error ranges of the sine wave signal and the cosine wave signal. sine wave signal squaring means for squaring the sine wave signal detected by said angle detector; cosine wave signal squaring means for squaring the cosine wave signal detected by said angle detector; adding means for adding the sine wave signal squared by said sine wave signal squaring means to the cosine wave signal squared by said cosine wave signal squaring means; judging means for judging whether or not the addition result by said adding means falls within a predetermined range; and abnormality detecting means for detecting occurrence of abnormality in said angle detector when said judging means judges that the addition result does not fall within the predetermined range, wherein the upper limit of the predetermined range is determined based upon respective error ranges of the sine wave signal and the cosine wave signal.