Why is it true that the cosine of 0 equals 1?

A cosine of a triangle is the length of the leg adjacent to a specific angle divided by the hypotenuse. Another way of putting it is that a cosine of an angle is x/r, or the x-coordinate of the endpoint divided by the distance of the endpoint from the origin. In trigonometry, if this angle were to be zero radians or zero degrees, the triangle would become a short, flat line pointing directly to the right. In that case, the distance of the endpoint from the origin and the x-value of this point are one and the same. Thus, the ratio between them is 1, and the cosine of zero is 1.

Also, the power series for cosine is as follows (where the angle is in radians):

cos(x) = 1 - x^2/2 + x^4/24 - x^6/720 - x^8/40320 + ...

(The denominators are the factorials of even numbers.) If you put x=0, you get cos(0)=1.