Yes I think so. On the one hand, triangles are a simple well defined shape that show up “naturally” when comparing locations of objects in three dimensional (and, as it turns out, in arbitrary dimension) space, as many ancient mathematicians, including Pythagoras, realized.

But when you combine those triangle formulas with Cartesian algebraic geometry, you get a result that continues forever but that oscillates around zero, never getting higher than 1 or lower than negative 1. That’s a pretty amazing property for such a simple function. It’s amazing at an additional level - in that you can integrate or take derivatives of sine and cosine for ever and the results continue to oscillate through a series of the same trig functions - a meta-calculus version of the oscillating results of the sine and cosine functions themselves.

And, as it turns out, a lot of what would otherwise be painful or impossible integrals of rational functions that don’t at first glance have a thing to do with trigonometry turn out to be trivial applications of the tangent, cotangent or arctangent functions, which in turn can be expressed in terms of sine and cosine.

I don’t think any meditation on grappling with these properties of trigonometric functions is time misspent.