All three are ratios which do not have units.
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sin stands for sine cos stands for cosine and tan stands for tangent
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
Zero. Tangent = sine/cosine. sin(0) = 0 and cos(0) = 1, so 0/1 = 0.
You can choose either or but tangent which is sin/cos seems to be the most common way.
In geometry a Tangent is a straight line that just touches the circumference of a circle.