VEHICULAR STEERING SYSTEM BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a vehicular steering system having a steering mechanism for steering the steerable road wheels of a vehicle in accordance with a value that is obtained by mechanically adding an auxiliary steering angle, which can be electrically controlled by an auxiliary steering angle superposition mechanism, to the steering wheel angle of a steering wheel steered by a driver. In particular, the invention relates to novel technical improvements for performing steering (intervention steering) to correct the steering operation of the steering wheel by the driver, and at the same time changing a transmission characteristic between the steering angle of the steering wheel operated by the driver and the steered angle of the steerable road wheels. 2. Description of the Related Art Conventionally, there has been well known a vehicular steering system in which an auxiliary steering angle superposition mechanism and a steering mechanism are interposed between a steering wheel and steerable road wheels of a vehicle, so that the steerable road wheels are steered by mechanically superposing an amount of auxiliary steering by an electric motor in the auxiliary steering angle superposition mechanism on an amount of steering of the steering wheel operated by a driver. A planetary gear mechanism, a differential gear mechanism, a harmonic drive or the like is used as the auxiliary steering angle superposition mechanism. In such a kind of vehicular steering system, there has also been proposed a technique that changes a transmission characteristic of the steered angle of the steerable road wheels with respect to the steering angle of the steering wheel (steering wheel angle) by the driver in accordance with the traveling condition of the vehicle (see, for example, a first patent document: Japanese patent No. 3518590). In the conventional apparatus of the above-mentioned first patent document, the transmission characteristic between a steering wheel angle θ h (steering angle of the steering wheel operated by the driver) and the steered angle of the steerable road wheels is determined based on the traveling condition of the vehicle such as the vehicle speed, the steering speed of the steering wheel, etc., and a target steered angle θ pref is also determined based on the steering wheel angle θ h and the transmission characteristic. In addition, a target auxiliary steering angle θ sref is determined based on a characteristic that is decided from the target steered angle θ pref and the mechanical construction of the auxiliary steering angle superposition mechanism. For example, in case where the auxiliary steering angle superposition mechanism is controlled to be driven based on the target steered angle θ pref, a sensor for detecting the steered angle θ p of the vehicle is used so that the auxiliary steering angle θ s of the auxiliary steering angle superposition mechanism is controlled to be driven so as to satisfy the following expression(1). θpref- θp = o • • • (1) Further, in case where the auxiliary steering angle superposition mechanism is controlled to be driven based on the target auxiliary steering angle θ sref, a sensor for detecting the auxiliary steering angle θ s is used so that the auxiliary steering angle θ s of the auxiliary steering angle superposition mechanism is controlled to be driven so as to satisfy the following expression (2). θ sref - θ s = o • • • (2) For example, a rotary encoder or the like is used as a sensor for detecting the steered angle θ p or the auxiliary steering angle θ s of the vehicle, as shown in the above-mentioned first patent document. The rotary encoder outputs two-phase pulse signals comprising a combination of "0" and "1", so the individual steered angle and auxiliary steering angle can be obtained by counting these pulse signals. However, when the pulse signals become unable to be obtained due to a break or disconnection of either of signal lines for the two-phase pulses, failure of the rotary encoder, etc., normal counting of the pulse signals becomes impossible in spite of an actual change in the steered angle θ p, so the detected value of the steered angle θ p or the auxiliary steering angle θ s does not change. Thus, in case of using the steered angle θ p or the auxiliary steering angle θ s that does not change due to the failure, it will become impossible to make the expression (1) or expression (2) hold if the driving control of the auxiliary steering angle superposition mechanism is performed based on the expression (1) or expression (2). Accordingly, the control of the auxiliary steering angle θ s to be superposed by the auxiliary steering angle superposition mechanism becomes abnormal, and as a result, there is a possibility that the steerable road wheels might be steered in a direction not intended by the driver. Thus, in the above-mentioned first patent document, in order to detect the break or disconnection of the signal lines and the failure of the rotary encoder, the steered angle θ p is calculated from the steering wheel angle θ h and the auxiliary steering angle θ s, as shown by the following expression (3). Whether the angle detection section is in failure is determined by comparing the steered angle θ p obtained from the expression (3) with a steered angle of the steerable road wheels that is estimated based on a difference between the speeds of right and left road wheels. However, according to such a determination method, failure can not be detected until when the steering in the direction not intended by the driver proceeds. It is necessary to separately or independently detect the failure of the rotary encoder at an early time in order to solve the above-mentioned problem, but the rotary encoder has all the combinations of two phase signals of "0" and "1", as stated above, so it is impossible to detect the failure of the rotary encoder from the correlation of the two-phase signals. As described above, in the conventional vehicular steering system, particularly in the first patent document, in order to detect the break or disconnection of the signal lines or the failure of the rotary encoder, the steered angle θ p is calculated from the steering wheel angle θ h and the auxiliary steering angle θ s, as shown by the expression (3), and compared with the steered angle estimated based on the difference between the right and left road wheel speeds, so there is a problem that failure can not be detected until when the steering in the direction not intended by the driver proceeds. In addition, there is also another problem that even if the failure of the rotary encoder is intended to be separately or independently detected at an early time, detection signals of the rotary encoder include all the combinations of two-phase "0" and "1" signals and hence it is impossible to detect the failure of the rotary encoder from the correlation of the two-phase signals. SUMMARY OF THE INVENTION Accordingly, the present invention is intended to obviate the problems as referred to above, and has for its object to obtain a vehicular steering system which, even upon failure of a rotation angle sensor used for controlling the driving of an auxiliary steering angle superposition mechanism, is capable of detecting the failure of the rotation angle sensor at an early time thereby to suppress steerable road wheels of a vehicle from being steered to a direction not intended by a driver. Bearing the above object in mind, a vehicular steering system according to the present invention has a steering mechanism for steering steerable road wheels of a vehicle in accordance with a steering wheel to be steered by a driver of the vehicle and an auxiliary steering angle superposition mechanism with an electrically controllable rotational member. The system includes: a steering wheel angle detection section that detects a steering angle of the steering wheel operated by the driver as a steering wheel angle; an auxiliary steering angle detection section that detects an auxiliary steering angle to be superposed by the auxiliary steering angle superposition mechanism; a vehicle travel state detection section that detects the traveling state of the vehicle; a transmission characteristic setting section that sets a transmission characteristic between the steering wheel angle and the steered angle of the steerable road wheels in accordance with the traveling state of the vehicle; a target auxiliary steering angle calculation section that calculates a target auxiliary steering angle to be superposed by the auxiliary steering angle superposition mechanism in accordance with the transmission characteristic; a driving control section that drives the auxiliary steering angle superposition mechanism so as to make the auxiliary steering angle detected by the auxiliary steering angle detection section coincide with the target auxiliary steering angle; and an auxiliary steering angle detection abnormality monitoring section that detects the presence or absence of abnormality of the auxiliary steering angle detection section. The auxiliary steering angle detection section includes: a rotation angle sensor that outputs sinθ and cos θ corresponding to a rotation angle of the rotational member as detection signals; a rotation angle calculation section that calculates the rotation angle of the rotational member based on the detection signals; a multi-revolution counting section that counts the number of revolutions per minute of the rotational member based on the rotation angle; and an auxiliary steering angle calculation section that calculates the auxiliary steering angle based on the rotation angle and the number of revolutions per minute. The auxiliary steering angle detection abnormality monitoring section detects the presence or absence of abnormality of the auxiliary steering angle detection section by monitoring the detection signals. According to the present invention, a vehicular steering system includes an auxiliary steering angle detection section that detects an auxiliary steering angle to be superposed by an auxiliary steering angle superposition mechanism, and an auxiliary steering angle detection abnormality monitoring section that detects abnormality of the auxiliary steering angle detection section. The auxiliary steering angle detection section includes: a rotation angle sensor that outputs detection signals comprising sin θ and cos θ corresponding to the rotation angle θ of a rotational member that constitutes the auxiliary steering angle superposition mechanism; a rotation angle calculation section that calculates the rotation angle θ of the rotational member based on the detection signals of the rotation angle sensor; and a rotation measuring section that measures the number of revolutions per minute of the rotational member. The auxiliary steering angle detection abnormality monitoring section detects abnormality of the auxiliary steering angle detection section by monitoring the detection signals of the rotation angle sensor. As a result, the abnormality of the auxiliary steering angle detection section can be separately or independently detected at an early time, whereby it is possible to suppress the steerable road wheels of a vehicle from being steered to a direction not intended by a driver. The above and other objects, features and advantages of the present invention will become more readily apparent to those skilled in the art from the following detailed description of preferred embodiments of the present invention taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a block diagram showing the overall configuration of a vehicular sterling system according to a first embodiment of the present invention. Fig. 2 is an explanatory view illustrating a map and for deciding the relation between a steering wheel angle and a target steered angle in case where a variable gear ratio mechanism is constructed by using the vehicular steering system of Fig. 1. Fig. 3 is a timing chart explaining the operation of an auxiliary steering angle detection section according to the first embodiment of the present invention. Fig. 4 is an explanatory view for explaining the operation of an auxiliary steering angle detection abnormality monitoring section according to the first embodiment of the present invention. Fig. 5 is an explanatory view showing abnormality detection ranges of an auxiliary steering angle detection section according to the first embodiment of the present invention. Fig. 6 is a block diagram schematically showing the overall configuration of a vehicular steering system according to a second embodiment of the present invention. Fig. 7 is a waveform chart showing normal detection signals of an auxiliary steering angle detection section according to the second embodiment of the present invention. Fig. 8 is a block diagram conceptually showing a mechanistic model for estimating the rotational direction of an electric motor from an amount of driving an auxiliary steering angle superposition mechanism according to the second embodiment of the present invention. Fig. 9 is a block diagram schematically showing the overall configuration of a vehicular sterling system excluding an auxiliary steering angle superposition mechanism according to a third embodiment of the present invention. Fig. 10 is a waveform chart showing detection signals in case of using a resolver as an auxiliary steering angle detection section according to the third embodiment of the present invention. Fig. 11 is a waveform chart for explaining in-phase signal processing of detection signals in case of using a resolver as an auxiliary steering angle detection section according to the third embodiment of the present invention. Fig. 12 is a waveform chart for explaining opposite phase signal processing of the detection signals in case of using the resolver as the auxiliary steering angle detection section according to the third embodiment of the present invention. Fig. 13 is a waveform chart for explaining the operation of an auxiliary steering angle detection abnormality monitoring section according to the third embodiment of the present invention. Fig. 14 is a flow chart illustrating termination processing for a multi-revolution count value by a multi-revolution counting section according to the third embodiment of the present invention. Fig. 15 is a flow chart illustrating start-up or activation processing for the multi-revolution count value by the multi-revolution counting section according to the third embodiment of the present invention. DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, preferred embodiments of the present invention will be described in detail while referring to accompany drawings. Embodiment 1. Referring to the drawings and first to Fig. 1, there is shown, in a block diagram, a vehicular steering system according to a first embodiment of the present invention. In Fig. 1, the vehicular steering system includes a steering wheel 1 that is steered by the driver of a vehicle, an auxiliary steering angle superposition mechanism 2 that is composed of two planetary gear mechanisms and an electrically controllable rotational member (to be described later), a steering mechanism 3 that steers steerable road wheels 5a, 5b of the vehicle according to the steering wheel 1 and the auxiliary steering angle superposition mechanism 2, and a pair of knuckle arms 4a, 4b that connect between the steering mechanism 3 and the steerable road wheels 5a, 5b, respectively. In addition, the vehicular sterling system according to the first embodiment of the present invention further includes an auxiliary steering angle detection section 6 that detects an auxiliary steering angle θ M to be superposed by the auxiliary steering angle superposition mechanism 2, a steering wheel angle detection section 7 that detects the steering angle of the steering wheel 1 operated by the driver as a steering wheel angle θH,a target auxiliary steering angle calculation section 8 that calculates a target auxiliary steering angle θ MREF to be superposed by the auxiliary steering angle superposition mechanism 2 in accordance with a transmission characteristic, a driving section 9 that drives the auxiliary steering angle superposition rudder mechanism 2 in such a manner that the auxiliary steering angle 9 M detected by the auxiliary steering angle detection section 6 coincides with the target auxiliary steering angle 9 MREF, a vehicle travel state detection section 10 that detects the traveling state of said vehicle, and an auxiliary steering angle detection abnormality monitoring section 11 that detects the presence or absence of the abnormality of the auxiliary steering angle detection section 6. The auxiliary steering angle superposition mechanism 2 is provided with a rotational member that is driven by the driving section 9, a first planetary gear mechanism 201 through 205 that is connected with the rotational member and the steering wheel 1, and a second planetary gear mechanism 206 through 209 that is interposed between the first planetary gear mechanism 201 through 205 and the steering mechanism 3. The rotational member of the auxiliary steering angle superposition mechanism 2 each comprises a worm gear 211, and an electric motor 212 that drives the worm gear 211. In the case of Fig. 1, the auxiliary steering angle detection section 6 detects the auxiliary steering angle θ M on the basis of the rotation angle of the worm gear 212 in the auxiliary steering angle superposition mechanism 2. Here, note that in the auxiliary steering angle superposition mechanism 2, the sum of the steering wheel angle θ H and the auxiliary steering angle θ M is5 in principle, equal to a pinion angle θ P (the rotation angle of the pinion gear 301 to be described later). In addition, the auxiliary steering angle is strictly a value that is obtained by multiplying the rotation angle of the electric motor 212 by Gs (the speed ratio from the worm gear 211 to the pinion gear 301 to be described later). However, detecting the rotation angle of the electric motor 212 is substantially equal to detecting the auxiliary steering angle, so in the following, the rotation angle θ M of the electric motor 212 is expediently handled as the auxiliary steering angle. The first planetary gear mechanism in the auxiliary steering angle superposition mechanism 2 is composed of a sun gear 201 connected with the steering wheel 1, a pair of planetary gears 202a, 202b supported by a carrier 203, a ring gear 204, and a worm wheel 205 for rotating the ring gear 204. The second planetary gear mechanism connected with the first planetary gear mechanism is composed of a sun gear 206, a pair of planetary gears 207a, 207b supported by a carrier 208, and a fixed ring gear 209. The carrier 203 of the first planetary gear mechanism and the carrier 208 of the second planetary gear mechanism are connected with each other through a shaft 210. The steering mechanism 3 is of a rack-and-pinion type, and is composed of a pinion gear 301 that is connected with the shaft 210, and a rack gear 302 that is in mesh with the pinion gear 301. The rotation of the pinion gear 301 is converted into a linear motion of the rack gear 302, and the linear motion of the rack gear 302 is converted into a steered angle of the steerable road wheels 5a, 5b through the knuckle arms 4a, 4b. The direction (steered angle θ w) of the steerable road wheels 5a, 5b is obtained by directly detecting the steered angle of the steerable road wheels 5a, 5b, or directly detecting the opinion angle θ P, or detecting the stroke of the rack gear 302. Here, there is illustrated, as an example, the case where the steered angle θ w is obtained by detecting the pinion angle θ P. The auxiliary steering angle detection section 6 includes a rotation angle sensor 601 that outputs, as detection signals, sin θ and cos θ corresponding to the rotation angle θ of the worm gear 212 in the auxiliary steering angle superposition mechanism 2, a rotation angle calculation section 602 that calculates the rotation angle θ of the worm gear 212 based on the detection signals sin θ , cos θ , a multi-revolution counting section 603 that counts the number of revolutions per minute n of the worm gear 212 based on the rotation angle θ, and an auxiliary steering angle calculation section 604 that calculates the auxiliary steering angle θ M based on the rotation angle θ and the number of revolutions per minute n. The target auxiliary steering angle calculation section 8 includes a transmission characteristic setting section 801 that sets a transmission characteristic between the steering wheel angle θ H and the steered angle θ w of the steerable road wheels 5a, 5b in accordance with the traveling condition of the vehicle. The auxiliary steering angle detection abnormality monitoring section 11 detects the presence or absence of abnormality of the auxiliary steering angle detection section 6 by monitoring the detection signals sin θ , cos θ , and stops the driving of the auxiliary steering angle superposition mechanism 2 by the driving section 9 when abnormality of the auxiliary steering angle detection section 6 is detected. The driving section 9 includes a target driving amount calculation section 901 that calculates a target amount of driving (e.g., a target current) on the basis of a deviation between the detected auxiliary steering angle θ M and the target auxiliary steering angle θ MREF, and a motor drive part 902 that drives the electric motor 212 in accordance with the target amount of driving. In Fig. 1, the steering wheel angle detection section 7 detects the steering angle θ H (the steering wheel angle) of the steering wheel 1 that is steered by the driver, and inputs it to the target auxiliary steering angle calculation section 8. The vehicle travel state detection section 10 detects the traveling condition of the vehicle, and inputs it to the target auxiliary steering angle calculation section 8. The transmission characteristic setting section 801 in the target auxiliary steering angle calculation section 8 sets the transmission characteristic of the steerable road wheels 5a, 5b to the steering wheel angle θ H based on the traveling condition of the vehicle. The target auxiliary steering angle calculation section 8 calculates, based on the steering wheel angle θ H and the transmission characteristic, a required auxiliary steering angle to be superposed by the auxiliary steering angle superposition mechanism 2 as the target auxiliary steering angle θ MREF. The driving section 9 drives the electric motor 212 in the auxiliary steering angle superposition mechanism 2 in such a manner that the auxiliary steering angle θ M detected by the auxiliary steering angle detection section 6 coincides with the target auxiliary steering angle θ MREF calculated by the target auxiliary steering angle calculation section 8. The auxiliary steering angle detection abnormality monitoring section 11 monitors the detection signals sin θ , cos θ of the rotation angle sensor 601 in the auxiliary steering angle detection section 6, and determines the presence or absence of abnormality of the auxiliary steering angle detection section 6 based on a relational expression "sin2θ + cos2θ = 1". The result of the determination of the auxiliary steering angle detection abnormality monitoring section 11 is input to the driving section 9, where the processing of stopping the electric motor 212 upon occurrence of abnormality of the auxiliary steering angle detection section 6 is performed. That is, when abnormality is detected by the auxiliary steering angle detection abnormality monitoring section 11, the driving control of the auxiliary steering angle superposition mechanism 2 is stopped. Next, further detailed reference will be made to the operation of this first embodiment of the present invention, as shown in Fig. 1. First of all, reference will be made to the state in which the worm gear 211 in the auxiliary steering angle superposition mechanism 2 is held stationary or is prevented from rotation. When the worm gear 211 is held stationary, the ring gear 204 of the first planetary gear mechanism is fixed. Under such a condition, when the driver operates the steering wheel 1, the torque of rotation thereof generated upon steering is transmitted to the sun gear 201 of the first planetary gear mechanism. The rotation of the sun gear 201 is transmitted to the planetary gears 201a, 201b, but at this time, the ring gear 204 is fixed, so the rotation of the sun gear 201 is converted into the orbital motion of the carrier 203 that supports the planetary gears 202a, 202b. Accordingly, the first planetary gear mechanism, serving to rotate the shaft 210 for transmission of rotation to the second planetary gear mechanism, functions as a speed reducer of a planetary gear type. The rotation of the shaft 210 is transmitted to the carrier 208 of the second planetary gear mechanism so as to rotate it, whereby the planetary gears 207a, 207b are driven to revolve around the sun gear 206 in accordance with the rotation of the carrier 208. Here, in the second planetary gear mechanism, the ring gear 209 is fixed, so the revolutions of the planetary gears 207a, 207b cause the sun gear 206 to rotate whereby the pinion gear 301 in the steering mechanism 3 is driven to rotate. At this time, the second planetary gear mechanism operates as a speed increasing gear, as viewed from the shaft 210. Accordingly, the rotation of the steering wheel 1 is mechanically transmitted to the pinion gear 301 in the steering mechanism 3 with a transmission ratio of "1 : 1". Note that the transmission ratio at this time becomes a value which is obtained by multiplication of the speed reduction ratio of the first planetary gear mechanism and the speed reduction ratio (speed increasing ratio) of the second planetary gear mechanism, and if the constructions of both of the planetary gear mechanisms are the same with respect to each other, the transmission ratio as a whole becomes "1". That is, in the construction of the auxiliary steering angle superposition mechanism 2 as shown in Fig. 1, it will be understood that if the rotation of the worm gear 211 is stopped, the steering system becomes an ordinary one in which the transmission ratio between the steering wheel angle θ H and the pinion angle θ P becomes "1 : 1". Now, reference will be made to the case where the electric motor 212 is driven to rotate the worm gear 211 with the steering wheel 1 being fixed. When the worm gear 211 is driven to rotate, the ring gear 204 is caused to rotate through the worm wheel 205. At this time, the rotation of the ring gear 204 is transmitted to the planetary gears 202a, 202b, but the sun gear 201 is fixed by the steering wheel 1, so the rotation of the ring gear 204 is transmitted to the shaft 210 through the carrier 203 as the revolutions of the planetary gears 202a, 202b. As the shaft 210 rotates, the steering mechanism 3 is driven to steer the steerable road wheels 5a3 5b through the second planetary gear mechanism, as stated above. Next, reference will be made to the case where the electric motor 212 is driven to rotate the worm gear 211 while operating the steering wheel 1. In this case, the auxiliary steering angle superposition mechanism 2 is constructed so as to be electrically controlled while responding to the steering wheel 1, so the following expression (4) holds from the above-mentioned expression (3) by using the steering angle of the steering wheel 1 (the steering wheel angle θH), the rotation angle of the electric motor 212 (the auxiliary steering angle θ M), the rotation angle of the pinion gear 301 (the pinion angle θ P), and the speed ratio Gs from the worm gear 211 to the pinion gear 301. θP= θH+ ΘM/GS • • • (4) Next, reference will be made, as an example of a specific operation of the transmission characteristic setting section 801 in the target auxiliary steering angle calculation section 8, to a variable gear ratio mechanism that changes the ratio between the steering wheel angle θ H and the steered angle θ w of the steerable road wheels 5a, 5b in accordance with the traveling condition of the vehicle while referring to Figs. 2 through Fig. 5. Fig. 2 is an explanatory view that illustrates a set map of the target steered angle (target steering angle) θ WREF, wherein there is shown the relation of the steering wheel angle θ H and the target steered angle ΘWREF upon construction of the variable gear ratio mechanism. In Fig. 2, one example of a map is shown which is used for calculating the target steered angle θ WREF with respect to the steering wheel angle θ H in accordance with the traveling condition of the vehicle (the vehicle speed in this example). As stated above, the steering wheel angle θ H of the steering wheel 1 by the steering operation of the driver is detected by the steering wheel angle detection section 7 and input to the target auxiliary steering angle calculation section 8. Also, the traveling condition of the vehicle is detected by the vehicle travel state detection section 10 and input to the target auxiliary steering angle calculation section 8. At this time, the transmission characteristic setting section 801 in the target auxiliary steering angle calculation section 8 calculates the target steered angle θ WREF based on the steering wheel angle θ H and the vehicle speed (the traveling condition of the vehicle) according to the map shown in Fig. 2. In addition, there is a predetermined relation between the steered angle θw of the steerable road wheels 5a, 5b and the pinion angle θ P of the pinion gear 301, so by using the relation therebetween, the transmission characteristic setting section 801 converts the target steered angle θ WREF into a target pinion angle θ PREF for the pinion gear 301 in the steering mechanism 3. Further, the target auxiliary steering angle calculation section 8 calculates the target auxiliary steering angle θ MREF by using the relation between the target pinion angle θ PREF and the above expression (4) through the calculation processing of the following expression (5). θ MREF = Gs (θ PREF - θH) • • • (5) Fig. 3 is a timing chart that explains a specific operation of the auxiliary steering angle detection section 65 wherein there are shown, as one example, individual signal waveforms when the auxiliary steering angle θ M corresponding to the actual rotation angle θ* of the electric motor 212 is detected. First of all, the rotation angle sensor 601 in the auxiliary steering angle detection section 6 detects the rotation angle θ of the electric motor 212 (or the worm gear 211) of the auxiliary steering angle superposition mechanism 2. At this time, the rotation angle sensor 601 outputs two detection signals corresponding to sin θ and cos θ , as previously stated. In Fig. 3, for example, if the actual rotation angle θ* of the electric motor 212 has changed in a sinusoidal manner, the detection signals sinθ, cos θ from the rotation angle sensor 601 take waveforms shown in this figure, respectively. Here, note that the amplitudes of the detection signals sin θ, cos θ are expediently described here as "1". As the rotation angle sensor 601, there may be used a variety of well-known sensors such as a resolver, a sensor for detecting the direction of a magnetic flux by using an AMR (anisotropic magnetoresistive element), etc. The detection signals sin θ , cos θ corresponding to the rotation angle 9 are input to the rotation angle calculation section 602 in which the rotation angle θ is calculated from these detection signals based on the following expression (6). θ =tan-1 (sinθ/cosθ) • • • (6) where the rotation angle 9 is a value within the range of 0° ≤ θ < 360° . Here, note that both sinθ and cos θ are periodic functions, and hence in the above-mentioned calculation processing, the rotation angle θ can be measured only within the range of from 0 degrees to 360 degrees, and it is not possible to detect the rotation angle θ corresponding to the actual rotation angle θ * in an accurate manner, as shown in Fig. 3. Accordingly, the rotation angle θ calculated by the rotation angle calculation section 602 is input to the multi-revolution counting section 603 in which the rotation angle 602a is processed in a time series manner thereby to count the number of revolutions per minute n of the worm gear 212. That is, as shown by arrows in Fig. 3, the multi-revolution counting section 603 counts up the number of revolutions per minute n (count value) when the rotation angle θ has changed from 360 degrees to 0 degrees, but conversely counts down the number of revolutions per minute n (count value) when the rotation angle θ has changed from 0 degrees to 360 degrees. The multi-revolution counting section 603 inputs the number of revolutions per minute n thus counted to the auxiliary steering angle calculation section 604. The auxiliary steering angle calculation section 604 accurately calculates the auxiliary steering angle θ M by using the number of revolutions per minute n from the multi-revolution counting section 603 and the rotation angle θ from the rotation angle calculation section 602, as shown by the following expression (7), and inputs it to the driving section 9. θM=nх360 + θ • • • (7) Not only the auxiliary steering angle θ M from the auxiliary steering angle detection section 6 but also the target auxiliary steering angle θ MREF from the target auxiliary steering angle calculation section 8 is input to the driving section 9. The target driving amount calculation section 901 in the driving section 9 calculates, based on a deviation between the target auxiliary steering angle θ MREF and the auxiliary steering angle θ M (detected value), a target amount of driving of the electric motor 212 in the auxiliary steering angle superposition mechanism 2 in such a manner that the following expression (8) can hold. θMREF- θM = O . . . (8) The target amount of driving is, for example, in the form of a target current to be supplied to the electric motor 212. The motor drive section 902 drives the electric motor 212 in accordance with the target amount of driving (the target current) from the target driving amount calculation section 901. Next, reference will be made to the operation of the vehicular steering system when abnormality occurs in the auxiliary steering angle detection section 6. When one of the two detection signals sin θ , cos θ from the rotation angle sensor 601 is not input to the rotation angle calculation section 602 due to a break, disconnection, etc., for example, as stated above, the auxiliary steering angle calculation section 604 can not output the accurate auxiliary steering angle θ M. At this time, if the driving section 9 drives the electric motor 212 based on the above expression (8) by using the inaccurate auxiliary steering angle θ M, the steerable road wheels 5a, 5b are steered in a direction quite different from the driver's intention. Accordingly, in order to avoid this, the auxiliary steering angle detection abnormality monitoring section 11 is arranged, as shown in Fig. 1, so that the detection signals sin θ , cos θ from the rotation angle sensor 601 are input to the auxiliary steering angle detection abnormality monitoring section 11. Specifically, the detection signals sin θ , cos θ are output in the form of physical quantities such as a voltage, a current, etc., in accordance with the characteristic of the rotation sensor 601. Fig. 4 and Fig. 5 are explanatory views that show the relations between the detection signals sin θ , cos θ output from the rotation angle sensor 601. As shown in Fig. 4, graphically representing the detection signals sin θ , cos θ in the form of a voltage output having an amplitude Vs with the cos θ and the sin θ being taken as the axis of abscissa and the axis of ordinate, respectively, a Lissajous circle is ideally formed (see a solid line). However, the rotation sensor 601 has individual variation or difference in its temperature characteristic, accuracy, etc., so the detection signals sin θ , cos θ , if output normally, have variation generated in the amplitude Vs thereof. Accordingly, the Lissajous circle drawn or formed by the normal detection signals sin θ , cos θ becomes between a lower limit circle (VthL to -VthL) and an upper limit circle (VthH to -VthH) on concentric circles with respect to the ideal Lissajous circle, as shown within the range of a broken line in Fig. 4. The auxiliary steering angle detection abnormality monitoring section 11 monitors whether the Lissajous circle formed by the detection signals sin θ , cos θ exists in the range between the lower limit circle and the upper limit circle. That is, a determination as to whether the following expression (9) is satisfied is made based on output voltages Vsin, Vcos of the detection signals sin θ , cos θ , respectively, a radius VthL of the lower limit circle, and a radius VthH of the upper limit circle. VthL2 < Vsin2 + Vcos2 < VthH2 • • • (9) When the above expression (9) is satisfied, the auxiliary steering angle detection abnormality monitoring section 11 determines that the auxiliary steering angle detection section 6 is normal, whereas when the above expression (9) is not satisfied, it is determined that the auxiliary steering angle detection section 6 is abnormal. For example, the case where the output voltage Vsin always becomes "0" due to the abnormality of the detection signal sinθ, an abnormality determination is made from the above expression (9) only when the following expression (10) is satisfied. Vcos