Sine and cosine of an angle defined using the unit circle. Think about that. You can determine every point along that Unit Circle knowing the radius and using Sin and cosine of that angle.
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@Lisa82 So covering a huge range of applications, then.
Among other things, I gather polar vectors are involved in Harmonic Analysis (of sound, vibration and electrical signals) and alternating-current electrical principles including for example the time delay between voltage and current in each cycle. They also bring in Complex Numbers as the sin and cosine become negative in some quadrants.