Assuming you do mean sin, it is the sine of an angle, the ratio of the opposite side to the hypotenuse in a right angle triangle with that angle.As the angle rotates through a full turn the sine oscillates between plus and minus one. (negative angles are the same as those that are more than half a turn.)

 That is useful in electrical calculations when considering the resultant of pairs of quantities that are orthogonal in time, such as the total current composed of both resistive and reactive current (in inductors and capacitors) One quantity can be represented as a sin wave and the other as a cosine wave , and the resultant complex quantity is the vector sum.

Apart from a few angles wtith simple geometry like 60 and 45 degrees, there is generally no simple method of calculation, but the value can be approximated by truncating the sum of an infinite series that converges, if the angle is expressed in radians,

Pre-calculator sin, cos. and tan were normally either a scale on the slide rule or available to higher accuracy in printed tabules, but nowadays electronic calculators approximate the values using Chebychev polynomials as these converge much faster than the 'correct' McLaurin series.

IF this is not quite what you wanted, and I fear it may not be, then rephrase the question and we can have another go.

Mike

Thank you for your explanation it's definitely explained a few questions but I was wondering where do we get these values in order to calculate the sin angel? Is it through appendix 4 of bs7671, where ratings for resistance, reactance and impedance are provided? 

Or is it normally provided on a motor plate such as the cos value? 

Thank you again for your previous explanation 

The real answer is, it's a combination of:

 - The supply impedance (resistance and reactance)
 - The cable impedance to the load (resistance and reactance)
 - The load impedance (resistance and reactance).

This will allow you to calculate currents and voltages at different points in the system ... and the phase angle difference between them.

So, what does a motor 'cos value' (power factor) tell you? It tells you the phase angle between the voltage and current, which you can use to determine the resistance and reactance of the motor, so you can include that in your calculations.

You might see some books use complex number notation to carry out resistance/reactance calculations. In this case, z=(r+jx) where j represents the imaginary number of the square root of negative 1 (mathematicians use i for this, but we use i for current).

There is nothing especially magical about cables greater or less than 16mm2, except that for larger cable sizes, the resistance drops but the inductive effects (the magnetic fields created around the wire ) tend to stay the same or get worse as the separation of flow and return current increases. In effect energy goes into creating that magnetic field inside the long thin coil formed by the live and neutral conductors, and then destroying and reversing it every half cycle, but unlike resistance, where the energy is lost to heat, the inductive energy is returned to the supply as the field collapses - so there is a maximum of inductively generated current flowing when the voltage crosses zero.
The tables of voltage drop represent this as two parts - the resistive bit, and the reactive bit - for thin cables, carrying lower currents, at least at 50Hz there is an assumption the inductive stuff can be safely neglected - indeed a quick squint at the tables shows that even when both are in the tables, it starts of with an R to X ratio that makes you think it was scarcely worth it. However, by cables of hundreds of sq mm it really is worth it, as the inductive part dominate.s

There is nothing especially magical about cables greater or less than 16mm2, except that for larger cable sizes, the resistance drops but the inductive effects (the magnetic fields created around the wire ) tend to stay the same or get worse as the separation of flow and return current increases. In effect energy goes into creating that magnetic field inside the long thin coil formed by the live and neutral conductors, and then destroying and reversing it every half cycle, but unlike resistance, where the energy is lost to heat, the inductive energy is returned to the supply as the field collapses - so there is a maximum of inductively generated current flowing when the voltage crosses zero.
The tables of voltage drop represent this as two parts - the resistive bit, and the reactive bit - for thin cables, carrying lower currents, at least at 50Hz there is an assumption the inductive stuff can be safely neglected - indeed a quick squint at the tables shows that even when both are in the tables, it starts of with an R to X ratio that makes you think it was scarcely worth it. However, by cables of hundreds of sq mm it really is worth it, as the inductive part dominate.s

So resistance and reactance can be seen as more indirectly proportional. And the fact that a smaller csa cable tends to have a lover current passing through it is the reason to which the reactance is lower due to the weaker Magnetic field been created would this be right?