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Math - why sin(0) is equal 0?
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The explanation why sin(0)=0 requires to refer to the function definition.
sin(α) has been defined as:
Let's suppose that: the alpha angle goes to zero (α -> 0).
It causes that: the opposite side goes to zero too (a -> 0) and the hypotenuse side goes to the adjacent side (h -> b). When the angle is equal to 0 and a is equal to 0 then 0 divided by h is equal to 0. It means sin(0) is equal to 0 according to the above definition.
Simple visualization is presented on the below picture:
