Question

Why is tan (0) = 0?

Answer 1

You may see this from either the definition of `tan` or from geometry.

Explanation:

1] the tangent is equal to the ratio `sin/cos` so if you have:
`tan(0)=sin(0)/cos(0)=0/1=0`
2] obseving the geometrical meaning of the tangent you have:

You can see that when `alpha` becomes very small or zero the length of the red segment, representing the `tan`, becomes small and eventually zero when `alpha=0`.

Hope it helps!