But it's trigonometry, not anometry. Really, the unit circle is important because it's the unit circle, not because it's the unit circle. A circle is 2π angles

But it's trigonometry, not anometry. Really, the unit circle is important because it's the unit circle, not because it's the unit circle. A circle is 2π angles. A triangle is composed of the same kind of angles, which means that, because the diameter of the circle doesn't matter (because it's a unit circle), then it's less important what the lengths are than it is how the lengths relate to one another. I.e., what factor of a unit vector as compared to what other factor of a unit vector.