I know it technically is -cos from a sinusoidal voltage. But what happens when voltage just starts its first cycle from 0V. The -cos gives current of -Imax just at time 0t. It just doesn't make sense.
Value-wise it is typically 6 times the full load current, this is because when you apply the supply voltage, the magnetic field rotates at 50HZ, but the rotor is stationary, therefore you are cutting maximum magnetic flux, and drawing maximum current. As the rotor speeds up, less flux is cut and the current drops, because the rotor is trying to catch up to the rotating field. The rotor can never catch the magnetic field because if it did, flux cut would be zero, hence current would be zero and the rotor would slow down. So the rotor typically runs at 2% less than the rotating field, this is called the slip speed. So a 2 pole motor that should theoretically have a speed of 3000rpm will actually run at about 2940rpm (2% slip). HTH
pbolton seems to think you mean a motor starting current. If you've expressed yourself clearly (which I believe to be case) then you mean the starting current on a pure inductance. As you say you might apply the voltage as sin. (staring from zero) then the steady state current would be -cos. However at the start we are faced with the problem that a current in an inductance cannot change suddenly. What happens is that a dc current component of +1 appears instantaneously in the coil to cancel the -cos, giving a net starting current of zero. The steady state -cos wave then proceeds superimposed on the +1 dc. The latter (starting transient) then slowly decays at the time constant of the coil (L/R) since it has no voltage to sustain it, leaving the -cos as steady state value. If the inductor and supply voltage had no resistance the d.c component would persist indefinitely. If you start the voltage at different points in the cycle the size of the transient dc component will vary but is always somewhere in the range -1 to +1.
