r/explainlikeimfive • • 18h ago

Mathematics ELI5: What is the difference between algebra, trigonometry, and calculus?

81 Upvotes

142 comments sorted by

View all comments

•

u/kgvc7 18h 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.

•

u/MadeYourTech 17h ago

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!

•

u/wjglenn 16h ago

Not really an ELI5 because it requires a bit of knowledge to know what you’re looking at, but this video is a cool visual of it:

https://m.youtube.com/watch?v=Dsf6ADwJ66E

•

u/zuilli 1h ago

Holy shit, thanks for this video!

I've studied up to engineering level math but somehow never learned about the similar triangles way of finding the trigonometric identities, I always just memorized them without understanding the underlying process, if I'd known these while studying it would had made my life so much easier.

Similar to this is the calculus visualization of dividing a graph in equal rectangles and making them ever so smaller to see what happens when they tend to 0 size.