Why are Sine waves used for electrical power transmission, and why using 50 or 60 Hz?

In addition to those answers: Regarding 1st part, I think that the most important thing is that Sin wave is used because its shape can't be changed to another (Differentiation & Integration) when traveling along transmission lines, so voltage and current waves and as a result the power will be the same among transmitting and receiving points.
Regarding 2nd part, also there is one extra reason which that voltage and current waves will be almost stable along transmission cables because wave length for 50 Hz will be 6000 Km, and for 60 Hz will be 5000 Km.

in addition to the last correct answer of eng/wassem we use sine wave in transmission of electrical power because the sin wave is an indicator to the alternative electrical power which is more and more easier in its generation by the meaning its the pure output of the transformers which uses for amplifying the rate of generated voltage to transmit it via overhead transmission line or underground cables to be reduced easily again near the distribution areas and also its more cheaper to transmit and distribute via sin wave electrical power because we don't need any combination or more electrical devices like ( inverters ) but we also tend to transmit the electrical power via dc form (not sin wave) when we transmit the power to another country has a different frequency rate or the lines travel extra long distances because it well known that the dc circuit has less power losses than the sin or alternative electrical power.
************************************************************************ And about the second part of question there's more than answer .
for abbreviation we can say that the frequency rate is depend to the country frequency standard rate because the machines , equipment , devices on this country of course has the same nominal frequency rate to operate more effectively .also there's another consideration must be taken for the frequency rate value and electrical phenomena depend on the frequency value like akin effect value

Sine waves used for electrical power transmission because it can be generated using normal copper windings in alternator rotors and stators .

sine wave is the most efficient waveform to use and also because it can be generated using normal copper windings in alternator rotors and stators without needing much, if any, "wave shape improvement" equipment.
because at very high frequencies the current no longer flows in the wire, but effectively flows on the surface of the wire, within a thickness of a few skin depths ( 50 - 60 HZ )

A sine wave is used for transmission (not a square or triangular wave) because a sine wave is the most efficient waveform to use and also because it can be generated using normal copper windings in alternator rotors and stators without needing much, if any, "wave shape improvement" equipment.
And why 50-60 Hz because at very high frequencies the current no longer flows in the wire, but effectively flows on the surface of the wire, within a thickness of a few skin depths.
The skin depth is the thickness at which the current density is reduced by 63%.
Even at relatively low frequencies used for power transmission (50–60 Hz), non-uniform distribution of current still occurs in sufficiently thick conductors.
For example, the skin depth of a copper conductor is approximately 8.57 mm at 60 Hz, so high current conductors are usually hollow to reduce their mass and cost.

The type of electricity delivered to homes and businesses was first direct current (DC) but then changed to AC electricity. The standard voltage level started at110V, went to240V, back to110V, and then to220V. The frequency started at60Hz and then went to50Hz in most areas.

sine wave developed according to the generator principle

It is generally accepted that "Nikola Tesla" chose60 hertz as the lowest frequency that would not cause street lighting to flicker visibly. The origin of the50 hertz frequency used in other parts of the world is open to debate

Sine waves used for electrical power transmission because it can be generated using normal copper windings in alternator rotors and stators. Agreed with Mohamed Shehata Mohamed

In alternating current (AC, also ac), the flow of electric charge periodically reverses direction.
In direct current (DC, also dc), the flow of electric charge is only in one direction.
The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.[1] [2] AC is the form in which electric power is delivered to businesses and residences.
The usual waveform of an AC power circuit is a sine wave.
In certain applications, different waveforms are used, such as triangular or square waves.
Audio and radio signals carried on electrical wires are also examples of alternating current.
In these applications, an important goal is often the recovery of information encoded (or modulated) onto the AC signal

Please all are requested to sequeeze their replies in their post to basic concepts.

 

Sine Wave, AC system can easily be Generated, Transmitted & Distributed over Long Values of KVAs & KMs with minimum Power Losses. Especially the role of Transfomers.

 

If you Understand Fourier transform / analysis method of Mathematics / Engineering then you must know that all periodic waves (Square, Triangular etc.) & also somwhat non-periodic waves are composed of sum of different sines waves of different amplitudes, frequencies & phases. Hence all waveforms are actually sine waves in background.

 

Now Question of50 Hz or60 Hz is so simple as Questions of:

 

Metric System / SI Units Systems

American Influence / British Influence