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Math - why sin(0) is equal 0?

11 points
Created by:
AnnLen
13450

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

sin(α) has been defined as:

Sine function definition.
Sine 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 a is equal to 0 then 0 divided by h is equal to 0. It means sin(0) is equal to 0 acording to above definition.

sin(0)=1 math explanation
sin(0)=1 math explanation

Simple visualisation is presented on below picture:

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