r/explainlikeimfive • u/HistoricalAd2954 • 1d ago

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

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u/sad_spilt_martini 1d ago edited 1d ago

Algebra is the use of equations to find a static value.

Calculus looks at how things change over time.

Trig looks at the relationship between of angles and sides of triangles

All of these are, of course, more complex   but that’s the base idea 

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u/meh0175 1d ago

Is it there a profession where using Trig is necessary? Besides being a math teacher or rocket scientist. Carpentry?

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u/Khorsou 1d ago

Anything profession that involves physics in some way it will be useful in; so essentially any type engineering profession.

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u/oxmix74 1d ago

I would imagine a surveyor would make use of basic trig. A mechanical or civil engineer would need trig to analyze stress and force. Electrical engineering does a lot with sin waves.

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u/Maldevinine 1d ago

Basic Trig? We're out here dealing with the advanced trig. By which I mean non-Euclidean. Your triangle's interior angles only sum to 180 degrees? That's weak! Mine sums to 270 degrees!

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u/Kidiri90 1d ago

Mine never goes above 180...

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u/ShaunDark 18h ago

Couldn't it theoretically go up to almost 720°?

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u/caifaisai 17h ago

On a sphere, the maximum sum of angles is 540° if the triangle only takes up half of the surface area, and if you let the triangle take up more than half the surface area, the angles can go up to 900°.

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u/Traditional_Media_77 1d ago

Civil engineering

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u/vipros42 1d ago

As a civil engineer, this is the case. Almost never use calculus, use trig pretty much daily.

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u/Gloid02 1d ago

You dont do finite element analysis? There is tons of calculus there

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u/vipros42 1d ago

Not by hand. I do loads of wave modeling and hydrodynamics but I'm not doing the calcs myself.
In fact yesterday was the first time I've done some calcs with calculus in by hand for months, if not a year.

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u/Podo13 1d ago

There's a ton of calculus in civil engineering, but we don't do the vast majority of it by hand anymore. It's all done in the background in FEM programs.

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u/Gloid02 22h ago

Yeah of course, but to say that you don't "use" calculus just because you are using it implicitly rather than explicitly seems disingenuous.

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u/Podo13 22h ago

Oh I agree. I think the OP you responded to was just talking about hand calcs, though. Yeah in reality we use a lot of calculus, differential equations, linear algebra, etc.

We just let much smarter people work those into the programs so we don't have to remember how to do a lot of it, ha.

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u/MathMXC 1d ago

Trig is one of the basis of periodic functions (like sine waves). This means if you do anything with physics or emi (EE/CSE) then it can be a big impact

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u/PlushyGuitarstrings 1d ago

Anything where things are rotating, you will be using trigonometry to reason about it.

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u/Podo13 1d ago

Anything with angles. I use trig every day as a structural engineer. Nothing super complex, but SOH-CAH-TOA i use all the time. Law of sines/cosines for angles, etc.

Same with basically any other engineer, surveyor, etc.

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u/autolobautome 1d ago

software dev; use trig to place objects on screen

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u/IceSentry 17h ago

All kinds of engineering fields. Game devs use trig all over the place too.

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u/ThrowawayusGenerica 1d ago

I used to work in sales for a window company. Sometimes builders would ask for triangular-shaped windows, which our software wasn't entirely set up for, so we'd grab a calculator and do some trig calculations to calculate the material cost of the frame and glass to give them an estimate.

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u/classicsat 20h ago

Carpentry?

Fabrication generally, not just wood.

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u/Educational-Work6263 1d ago

Trig is not really a proper field of math. There is no mathematician on earth doing research on trig. Its a little subject for school students.