Mathochism: The elegance of sines

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

Over the past two weeks, we’ve been studying trigonometry. We started with triangle trig (spasiba, Uchitel, for ensuring I learned those 30-60-90 and 45-45-90 triangles last semester!), then moved on to the unit circle (thank you, summer pre-calc prof, for helping make that less confusing the second time), then onto graphs of the various trig functions.

I’ve written before of my lack of enthusiasm for graphs, but I must make an exception for trig graphs (and parabolas and hyperbolas, which are rather cool). What can I say? I’ve always loved water, and waves, and both the sine and cosine functions graph as glorious waves, oscillating back and forth over the x axis, making me want to dive in.

Tangents don’t graph as waves, but as curved vertical lines that look a bit like cilia on a one-celled organism. Cotangents are the same, only in the opposite direction. Graph them together and they look like long, waving stems of grass.

Secants and cosecants float in space and are shaped like parabolas. They look like they’re about to drift away at short notice.

I have no memories of trig graphs except recent ones (during the summer class, I audited at least one class on them), and I have only vague memories of trig, the main one being SOHCAHTOA.

SOHCAHTOA is one of those invaluable mnemonics, like PEMDAS or FOIL, that make math less befuddling. But apart from that, I fear I never appreciated trigonometry.

I do now. There’s an elegance to it, even beyond the graphs. It’s also useful. I never really considered how mountains were measured before we had satellites or airplanes. Surveyors then did it with triangulation, which uses trigonometry, and were astonishingly accurate — within a few feet.

And triangulation is often used while navigating airspace (though VORs are being phased out by GPS), so I really appreciate that.

I do hope I won’t sour on trig, since it looks like sines and cosines will figure largely next semester in calculus. In the meantime, I’ll continue to be mesmerized by its lovely graphs.

All text copyrighted by A.K. Whitney, and cannot be used without permission.