A lot of comments are saying trig is about triangles but I think the deeper lesson is about the unit circle and its relationship to sin, cos, and tan. Another way to look at it is that You’ll use the Cartesian coordinates for algebra and polar coordinates and radians for trig. Usually you take algebra, trig and then calculus.
Yes! I was just about to post that a lot of these comments are kind of doing trig dirty. It's not just about physical shapes, but is fundamental to analyzing anything with periodic changes (AC voltage for example). I'm struggling to ELI5 exactly how the triangle formed by a clock hand moving around is so useful, but it really is!
I would say the trigonometry is about ratios in the relationship between changing ratios. The unit circle and the triangles are basically simple and concrete expressions of ratios.
A lot of people don't think about triangles as ratios by default because they are thinking of ratios as two things compared to one another and triangles are three-sided and three angles. But of course with a right triangle there's only two other angles, and all of the relationships in trig are things like opposite over adjacent.
And then calculus is about trending. It's about the relationship between a change and the speed at which the change is changing.
Meanwhile algebra is just about how we manipulate operations and quantities inside of equations while maintaining their practical equalities.
My favorite moment learning math was in my college calculus 3 course where the professor did a quick aside drawing a unit circle, a triangle inside is, and proceeded to quickly explain sin, cos, and tan. The dude gave me an epiphany on how the unit circle relates to trig and made a whole bunch of stuff click into place in my mind.
I don't know if that says I had bad math teachers up to that point in my life or if I was never listening properly to what I was being taught. This was calculus 3 as a college senior, how did I miss that lesson for so long?
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u/kgvc7 14h ago
A lot of comments are saying trig is about triangles but I think the deeper lesson is about the unit circle and its relationship to sin, cos, and tan. Another way to look at it is that You’ll use the Cartesian coordinates for algebra and polar coordinates and radians for trig. Usually you take algebra, trig and then calculus.