Math - why cos(0) is equal 1?

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Explaination why cos(0)=1 requires to refer to the function definition.

cos(α) has been defined as:

Cosine function definition.

Lets suppose that: alpha angle goes to zero (α -> 0) and adjacent side is constant (b = const).

It causes: opposite side goes to zero too (a -> 0) and hypotenuse side goes to adjacent side (h -> b). When angle is equal to 0 and b is equal to h then b divided by h is equal to 1. It means cos(0) is equal to 1 acording to above definition.

cos(0)=1 math explanation
cos(0)=1 math explanation

Simple visualisation is presented on below picture:

Why cos(0) is equal to 0? - explanation
Why cos(0) is equal to 0? - explanation
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