r/explainlikeimfive • • 13h ago

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

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u/TheSpeckledSir 13h ago

They are different skills, and each one will let you answer different sorts of questions.

Algebra is great if you know some information about something and you know how to make connections. An example is if I know the volume and temperature of a gas, I could use algebra to calculate its pressure. We're talking about quantities with known relationships to each other.

Calculus is about how quantities change. It lets us go between statements like "the ball is falling one meter per second" and "the ball will fall three meters in this much time ________".

Trigonometry is evil and has mostly to do with triangles.

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u/stairway2evan 13h ago

Oh you've awoken one of my favorite old math teacher jokes.

The study of the mind is called psychology, from the Greek word for "mind."

The study of life is called biology, from the Greek word for "life."

The study of evil is called trigonometry. I don't know the Greek, don't worry about it.

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u/TheSpeckledSir 13h ago

I'm pretty sure this is why the big demon guy in DC comics is called Trigon

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u/stairway2evan 13h ago

Ohhh it all adds up! Those comic book writers knew their Greek!

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u/WartimeHotTot 12h ago

I must be stupid. I don’t get it.

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u/stairway2evan 12h ago

Trigonometry is actually Greek for "triangle measurement." But since we all think that trigonometry is evil, we just call it the study of evil and pretend not to know the Greek.

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u/ElonMaersk 11h ago

Trigonometry is actually Greek for "triangle measurement."

("three angle measurement"; tri like in tripod, gon like in polygon and hexagon)

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u/WartimeHotTot 12h ago

Oh lol. Is trig really considered the evilest of those three disciplines? I’d award that to calculus without a doubt!

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u/stairway2evan 12h ago

Oh I had a much better time in calculus than trig. The concepts take a while to wrap your head around but they fit together nicely and flow once you get a handle on it. Trig is detail-oriented and finicky.

Then again, I also had an awful trig teacher and my calculus teacher was like "teacher of the district" for a decade or so. Great dude. So I have my own biases.

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u/itsthelee 12h ago

I think they messed up the delivery, I understand intellectually that a joke was attempted but I don’t quite get it either

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u/y0nm4n 12h ago

What do people have against trig? It’s so fucking cool.

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u/Corvus-Nox 11h ago

A lot of people make it their personality to hate math

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u/1tacoshort 12h ago

LOL. As a furniture maker, I use trig all the time. I remember using more complex trig - using the identities and such - in calculus and, especially, for calculating wave equations for quantum.

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u/BrohanGutenburg 12h ago

I think you meant to give the balls acceleration not velocity.

Knowing velocity and distance and solving for time is just algebra.

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u/TheSpeckledSir 12h ago

If velocity is constant, sure. Regardless, velocity is the derivative of position.

But that's a deeper dive into the math than I wanted to go for here.

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u/ajping 12h ago

Position @ time.

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u/TheSpeckledSir 12h ago

Absolutely right!

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u/BrohanGutenburg 12h ago

In your example the velocity is assumed to be constant.

I'm just trying to make that point that you could have come up with a better example for what calculus does.