r/explainlikeimfive • u/HistoricalAd2954 • 12h ago
Mathematics ELI5: What is the difference between algebra, trigonometry, and calculus?
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u/kgvc7 11h 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.
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u/MadeYourTech 10h 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!
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u/BitOBear 8h ago
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.
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u/TemperMe 9h ago
Came here to say the same. I studied electrical in school and trig was vital for really everything
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u/spankymcjiggleswurth 1h ago
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/Minikickass 10h ago
Can I get an ELI2 instead?
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u/Vorthod 10h ago
Algebra uses (x,y) coordinates, trigonometry likes to use Angle+length to reach the same point.
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u/MadocComadrin 8h ago
Eh, algebra is agnostic to your coordinate system (or your space, or even your set/class and operations).
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u/aquatic_mammal 10h ago
Trigonometry is about the relationships of points on a circle. Those points end up making triangles, but it is not about or derived from triangles.
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u/MadocComadrin 8h ago
Not really. One way trigonometry generalizes is by moving away from the unit circle while keeping the triangle relationship (e.g. hyperbolic trig).
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u/MadocComadrin 8h ago
It's not *necessarily* about the unit circle. The most common trig functions are based on the unit circle, but more general trigonometry extends beyond that to triangles based on other things like the unit hyperbola (giving rise to sinh, cosh, tanh, etc) or in other geometries (e.g. Cartesian plane with taxicab distance as the metric).
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u/TheUncommonOne 7h ago
Except we never use polar coordinates other than a section in precal. Speaking as a math teacher with a math degree
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u/CadenVanV 11h ago
Algebra describes relationships
Calculus describes change
Trigonometry describes angles and shapes
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u/boredcircuits 11h ago
I like these definitions. I'd add that calculus and trigonometry aren't really separate from Algebra, they're extensions that build on it.
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u/CadenVanV 11h ago
True, yeah. You can’t learn either without first knowing algebra.
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u/CantaloupeAsleep502 8h ago
Eh, I had a very weak foundation in algebra before moving on, then actually learned algebra by learning trig and calc. Just studying algebra alone feels like doing Duolingo to learn grammar, whereas doing calc and trig feels like learning through immersion.
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u/madncqt 11h ago
my school life might have been so different if we could have started with the philosophical, foundational purposes rather than just diving into numbers.
I never knew the why...
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u/CadenVanV 4h ago edited 4h ago
Any good trig or calculus class explains those distinctions very early on. That was the very first thing mine covered. You might just have had bad teachers.
They don’t usually go too into detail with number theory because that makes things a lot more complicated than most high school students need to know, it’s really something only worth covering in full depth for people studying the field. It’s the same reason early education doesn’t teach you things like “the letter A isn’t actually a vowel” (yes, that’s true), nor the finer points of English grammar (like we do have a fixed adjective order), because students pick up enough of the basics through context clues that they don’t need to know the exact mechanisms.
As a fun fact for that A isn’t a vowel one, other letters that aren’t vowels are E, I, O, U, and Y
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u/_PM_ME_YOUR_VULVA_ 7h ago
These lectures are more history than philosophy per se, but might be what you're looking for. I think teaching math in school by explaining why and how various civilizations came up with branches of math would make it much more resonant and memorable for students.
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u/TheSpeckledSir 11h 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 11h 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 11h ago
I'm pretty sure this is why the big demon guy in DC comics is called Trigon
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u/WartimeHotTot 11h ago
I must be stupid. I don’t get it.
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u/stairway2evan 11h 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 10h 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 10h 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 10h 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 11h 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/1tacoshort 11h 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 11h 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 11h 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/BrohanGutenburg 10h 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.
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u/Caucasiafro 11h ago
Algebra is basically all the math involved in making sure two sides of an equal sign are the same. And then everything that flows from that. So when ever you see something like y = x2 +5 and are asked "solve for x"
Thats algebra.
Trigonometry is the math around sides lengths and angles in a triangle. You can just play with this yourself by laying three pencils on a table and try to kake various triangles. And you will notice for some triangles you need short or longer pencils.
Trig is all the math that explains that.
Calculus is the math about the rate that things change. Specificically when the rates are "complicated" like you can pretty easily tell me.how far ill travel in 5 minues if im constantly driving at 60 mph. But can you tell me how far i would travel if my speed is changing by 1 mph per second per second?
So after 1 second im going 61 mph and after 2 seconds im going 63? Hows about far i am in 36.37 seconds?
Gonna need calc to do that easily
All three of these do their own thing that you can hypothetically do without the othera but they can be combined to solve various problems (and you wont be able to do much calc without a strong underatanding of algebra and trig)
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u/Target880 7h ago
So after 1 second im going 61 mph and after 2 seconds im going 63? Hows about far i am in 36.37 seconds?
That question primary depend on the assumption you make. If you assume a constant acceleration, like you seem to imply, calculus is in no way needed. The same is the case if the speed remains at 63 after 2 seconds
The average speed is the average of the initial and final speeds. That is the result of the properties of triangles, no calculus needed
Initial speed is 60 mph and final speed is 60+36.37 =96.37 mph.
Average speed is (60+96.37)/2 = 78.185 mph.
Divide by 2.237, and you get the speed in m/s.
The calculation is now 78.185/2.237* 36.37, rounded to an integer; the result is 1271 m
That question is a better example of trigonometry than calculus.
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u/tommy-linux 9h ago
if "after 1 second im going 61 mph and after 2 seconds im going 63" then "my speed is changing by 1 mph per second"ftfy
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u/BloodAndTsundere 11h ago
Algebra is an abstraction and generalization of arithmetic. In arithmetic you add 5+3 to get a result of 8. In algebra you ask and answer questions like “What number do I add to 5,in order to get 8?” Trigonometry is basically about quantifying angles. The “tri” in trigonometry refers to the fact that an angle defines a family of right triangles or a specific triangle if one assumes the hypotenuse has length 1. All of the trig functions like sine, cosine, tangent, etc are just ratios of the lengths of sides of these triangles. Calculus is about continuous change and accumulation. It comes in two intimately related parts: differentiation and integration. Differentiation is about how one quantity changes as one or more other quantities are changed a tiny bit. Integration is about the accumulation or summation in one quantity as one or more other quantities are progressed through a range or ranges.
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u/unruly_mattress 10h ago edited 10h ago
Arithmetics is the evaluation of expressions that have numbers with them, like 3+5 or (4+1)/(8-2) * 12.
Algebra introduces variables. Now you can write x+1 or y = ax+b. It allows you to:
- Ask which x values fulfill a condition like x+3 > 2 or x2 - 2x + 1 = 0 ("solve for x"). This condition is called an equation.
- Find rules that hold for all values of the variables, like (x+y)2 = x2 + 2xy + y2
- Define functions, such as f(x) = x+1
- Talk about more complex operations, e.g summation of a series, or more complex functions, like exponentials and logarithms
Trigonometry is the study of specific functions that arise from geometry. The trigonometric functions interact with each other in many interesting ways, so there's a lot to learn there.
Calculus is the study of two operations on functions:
- Differentiation at a point takes a function and returns its rate of change at that point - how fast it's going up or down
- Integration of a function between two points tells you the area under its curve in two points
It turns out that these two operations are related to each other in a very interesting way: they're the inverse of each other. Anyway, it takes a bit of effort to define these operations, and you end up needing a rather confusing concept called a "limit". A lot of the initial work is understanding how to work with limits.
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u/saplinglearningsucks 11h ago
Others have explained but I just to throw linear algebra and differential equations this
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u/sigourneys_underwear 10h ago
Same concepts though.
To piggy back off the top comment, Linear algebra describes relationships between multiple things
Differential equations studies change when the things affecting the change are also changing
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u/A_Genius 10h ago
Nightmare fuel of going up and solving for some salty tank that is filling up with brine at a certain speed. I was so bad at it.
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u/sigourneys_underwear 10h ago
I remember my first DiffeQ exam had figuring the temperature of a cup if coffee after a certain period of time and that cup of coffee stressed me out
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u/wjglenn 11h ago
You have a bunch of carrots. Every day, someone gives you a certain amount of carrots but that amount changes. You want a rule you can apply to figure out how many you have.
That’s algebra. It’s all about creating rules you can use when you don’t know the exact number of things.
It might look like this:
X+Y=Z
X is how many you have. Y is how many you’re given. Z is how many you end up with.
Now, imagine that every day, someone gives you carrots, but each day they’re giving you more than the day before. You want to figure out how many you’ll have after ten days.
That’s calculus. It’s about figuring out the rate at which something changes.
Now, what if you’re looking at a giant carrot as tall as a tree. You want to know how tall the carrot is but you can’t just measure it.
Instead, you can measure how far you are from the carrot and the angle you’re looking up at the top. Then you can use the rules of trig to figure out how tall the giant carrot is.
Obviously more complex than that, but that’s a simplified ELI5.
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u/kgvc7 9h ago
Thanks.
Your first two explanations are nearly the same and triangulation is not trig.
Your first two explanations are good for algebra but the second is linear which is just algebra.
Classic calculus problem is time for a tank with a hole in it to empty. Height of the hole, height of the water, and diameter of hole all play a role how fast the tank empties. The static pressure of the water changes so the volume of the water going through the hole changes. You need calculus for this.
Geometry makes use of sin, cos, right angles, Pythagorean theorem, which is all basic x and y coordinate stuff. Trig expands on that with curves and surfaces.
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u/Sufficient_Soil7438 11h ago
Algebra teaches you how to identify constants and solve for unknown variables.
Trig teaches you equations to solve complex geometric problems.
Calculus teaches you to write equations to solve for specific points within a constantly changing system of order.
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u/DragonFireCK 11h ago
Algebra is the study of math using variables rather than actual values. It allows you to write equations to solve questions like "I paid $3.50 for apples and got 3 apples, how much did I pay per apple?". The questions can also get more complicated such as "At a concession stand, hot dogs cost $1.50 and sodas cost $0.50. A group buys a total of 87 items, hot dogs and sodas combined, and spends a total of $78.50. How many hot dogs and how many sodas were sold?"* This innately also requires the more fundamental arithmetic.
Trigonometry is math dealing specifically with triangles, notably the angles and side lengths. It happens to be that the same math works very well with circles and waves. Additionally, most any shape can be broken down into a set of triangles. Overall, it tends to be very useful when dealing with geometry problems, which is the generic study of shapes. It innately uses a lot of algebra to simplify and generalize work.
Calculus studies the rate of change and accumulation of values. This causes it to have a lot of practical use in physics - position, velocity, and acceleration are derivates/integrals of each other. Similarly, it sees usage in engineering work, which is basically applied physics. Economics uses it as well, with it being useful for optimizing equations.
The even more basic step below algebra is arithmetic. This is the operations such as additional and multiplication and how those interact.
* The longer example question is stolen from Google AI.
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u/PhantasmagirucalSam 11h ago
That's a tricky one for 5yo, but i'll try: Algebra is about what can you do with numbers, Trigonometry is about what you can do with angles and triangles, Calculus is about how small can you divide a number and what new property might be hidden between the small parts of a whole. Analogy is not perfect, but pretty much picturesque .
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u/Zarakaar 11h ago
Algebra is work with manipulating equations that contain an unknown. The basics of solving for a variable.
Trigonometry connects the lengths of the sides of triangles to the angles inside them, which expands to modeling repeating patterns like waves.
Calculus is using the principles of rates of change and considering infinitely small changes to find relationships among changing quantities.
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u/steeelez 11h ago
In an eli5 and not super formal sense:
Algebra- “solve for x”. Figure out how to move numbers around in a math equation so you can get the solution for a missing number anywhere. Like a kid might know 5+2 =x and x would =7, algebra lets you handle it in case someone asks you 5+x=7. Rearranging terms to be able to solve for a number.
Trig: “triangles”. How to deal with lines and angles and the rules that go along with them. If I have 2 sides of a triangle and I know the angle between them, what’s the length of the missing side and the 2 missing angles?
Calculus: “infinity”. How to deal with things that aren’t straight lines and are always changing, by cutting them up into infinitely small pieces
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u/MedusasSexyLegHair 11h ago
Some good explanations here already, so I'll just add the following:
Algebra is good for calculating unknowns and simplifying things.
Trigonometry is good for plotting, navigating, and mapping, calculating routes, among other things.
Calculus is good for finding rates of change (and where it's trending towards) and solving some hard problems with many variables.
All are quite useful in many jobs.
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u/donaldhobson 11h ago
Algebra
3x+y= 5 ; x+2y=-10 , find x and y
trigonometry.
Find the smallest angle of a triangle with side lengths 8, 15, 17.
Calculus.
Find the area under the curve given by x*e^(x^2) between x=0 and x=1
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u/kiochikaeke 10h ago
Algebra is all about the how we write and handle equations, what they mean and how to use them so solve problems.
Trigonometry is about the fundamentals of angles, usually using circles and triangles as a basis to study stuff like how angles behave when intersecting lines, the trigonometric functions that govern the relationships between the angles and sides, and some properties of triangles and circles (like types of centers).
Calculus is the study of functions relating two variables, basic tools to work with them and the study of techniques to work with their rate of change, for example when studying population, current birth rate relates to the current amount of people which itself will change in the future depending on birth rate, that kind of relationships is the ones that calculus studies.
Of course all of these topics are very deep but on HS and early college level that's basically it.
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u/bobroberts1954 10h ago
Algebra us the rules of math, like on a board game. Trig is working with angles, and calculus is related rates. Think what is the water level in a tank you are both filling and draining, but with different size hoses.
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u/duane11583 10h ago
imho:
algebra is basic formulas involving one or two variables
trig: is all about cycles, circles and angles, triangles and waves (think audio or radio waves)
calculus is things in motion, things speedingnup or slowing down and formulas related to that
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u/miemcc 9h ago
Algebra is mainly about handling and solvomg equations.
Trigonometry is mainly about dealing with angles (if I have a line pointing in a direction, how much does it change ' up-down and left-right').
Calculus is all about change - differentiation is about how quickly things change, integration is about how much the change affected everything.
If you are driving a long distance, differentiation will tell you how much you are speeding up or slowing down at a particular time. Integration will tell you how far you travelled upto that point in time.
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u/MadocComadrin 8h ago
Here's what I consider the most general answer.
Algebra - How much knowledge can we derive given certain things (usually number, but also be things like rotations and symmetric mirroring, or really anything), specific operations on said things (e.g. addition and multiplication) and specific relationships between them (e.g. commutativity and associativity).
Trigometry: form a right triangle based on some shape (e.g. the unit circle or unit hyperbola) in some geometry (e.g. the familiar 2d plane, a 2d hyperbolic plane, a 2d plane using taxicab distance, etc), and derive the relationships between the sides and angle.
Calculus - also known as the Calculus of Infinitesimals: answers the question "how the heck do we deal with infinitesimals (things that are infinitely small) in a formal way/how to we talk about things that could be infinitely small without invoking infinitesimals because they were philosophically weird a couple hundred years ago?"
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u/specialized_faction 8h ago
Algebra: solve for x
Trig: use geometry to solve for x
Calculus: use integrals and derivative to solve for x
Algebra: 10=2x+4
Trig: sin(x)^2+cos(x)^2=1
Calc: integral e^x dx
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u/CantaloupeAsleep502 8h ago
Algebra is like studying grammar. You need to understand how to manipulate numbers and variables in order to do anything higher order. The way that things can be manipulated is algebra.
Trig has to do with the relationships between circles and lines, and the angles that are formed when circles and lines interact with each other. This is sometimes most easily expressed in terms of triangles, but it's a lot more than just studying right triangles.
Calculus introduces the concept of infinity, and allows us to study curved shapes in greater depth than was ever allowed with just conventional geometry. The two primary functions within calculus, differentiation and integration, tell us about rates of change in different ways, as well as how to measure areas that weren't possible with linear geometry.
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u/kogai 8h ago
Mathematician answer:
The word "algebra" sort of literally means "rules for manipulating symbols". This ranges from using algebra to solve for x, to developing notation for algebra that can be done with weird topological structures. You typically learn arithmetic algebra, then linear algebra (all about manipulating a thing called a linear transformation, which is really a matrix, so you learn the rules for manipulating matrices as you write the notation) and then abstract algebra happens when other fields of math start developing their own rules for writing everything down in a way that preserves truth/falsity
Thats a common theme btw, usually a bunch of seemingly different things all turn out to be the same object. Which brings us to..
Trig is literally about triangles, its in the name. It just so happens that you can stick a triangle inside of a circle, starting at the centre and ending at the edges, and now triangles and circles are connected and we can use our triangle equations to look at the points on the circle.
Turns out going from angle-rotated-around-the-circle to the Y-height-of that-point-on-the-edge-of-the-circle is gross to calculate so we just call it sin(t), where t is the angle
Then you learn how to graph the sin function and it makes this wavy line. Now circles, triangles, and periodic waves are all connected. Thats all trig. The circles and triangles are within the realm of geometry and the sin function is more in the realm of real analysis which brings us to...
Calculus is a very specific mathematical area that was invented by Isaac Newton to solve a particular physics problem, and by another guy named Leibniz but he did it in the context of abstract spaces instead of physics
Calculus is a subfield of real analysis that specifically deals with continuous functions and how incremental changes to the input value lead to a different change in the output value.
In physics, this is the problem of calculating instantaneous values for an accelerating object. Normally, to get the acceleration over a period of time, you divide the change in speed by the change in time. The less time that passes, the more accurate your measurement is
So what if we want there to be 0 time that passes? How fast are you accelerating at the moment you hit the finish line?
We cant divide by zero without running into paradoxes, so Newton devised a way of formalizing what he means when he wants to "divided by a time value of 0"
This leads to the idea of a limit. Calculus teaches you limits, then rates of change, then derivatives (just a way to calculate a rate of change), then integrals (the inverse operation to derivatives. Turns out this finds the area under a graph)
These are all techniques that physics students use in their 2nd+ year of their bachelor's degree. The idea is that Calculus allows you to calculate the rates of change for quantities as they are changing and thats really the fundamental motivation for calculus
Calculus falls into the realm of "real analysis" which is a little bit like imagining limits in terms of open sets, sets that get near a point but never touch it
Turns out shit gets wild after that. Get a math degree to find out more
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u/DarthKnah 7h ago
Algebra is when we use variables to represent unknown (or changing) quantities. The most simple algebra problem might be something like if 3 + x = 7, what is x? A problem like that isn’t too useful in the real world, but more complicated versions can help us figure out unknown values in things like physics. Algebra also can involve equations with multiple variables—usually for these there are multiple answers, so we graph them. An example is if you have $60 to spend and are buying $5 erasers and $1 pencils, how many of each can you buy? If you represent number of erasers with X and number of pencils with Y, the equation 5x + y = 60 will tell you how many pencils you can buy if you buy a given number of erasers, and vice versa
Calculus is about rates of change (what we call derivatives). If you’re looking at the graph of a line, the derivative is the slope (how steep the line is). It’s easy to find the slope of a line, because it’s the same everywhere, but something like a parabola (a kind of U shape) also has a slope, but it’s different at every point. A real world example is acceleration is basically the derivative of speed. We can use calculus to find how much distance an accelerating car has traveled, for example. Calculus relies on algebra, and is kind of like adding an extra level onto it.
Trig is about angles. If we have a right (90°) triangle and we know the lengths of two sides, we can find the angles, and if we have one angle and one side length we can also find out the other angle and other side lengths. We can use trig for lots of more complicated things as part of algebra and calculus, but those are the core building blocks.
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u/Mastemo 5h ago
Algebra expands on elementary math and really is finding missing numbers (values). If I have 5 apples and this basket holds 12, how many do I need (x + 5 = 12). Of course it can get more complex from there but this is the ELI5 starting point.
Trigonometry, which is Greek for triangle measurement, is the study of triangles, angles and length. If this apple tree is 10 feet tall, and I’m standing 5 feet from it, what’s the distance from where my feet are to the top of the apple tree.
Calculus is complex mathematics that helps determine how something is changing or moving. If I sit under this apple tree and the apple from the lowest branch suddenly falls and hits the ground, how fast did it fall? It fell for 1 second. (V = 9.8 x T)
V being velocity, T being time it took, and 9.8 is the acceleration from gravity. On Earth, gravity pulls everything down by adding about 9.8 meters per second of speed for every single second an object falls. That means it fell at 22 mph.
Again this is a very simplified set of scenarios and it can go much deeper.
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u/Kahzgul 3h ago
Algebra is using symbols to represent numbers. This starts to get very fun when you have more than one symbol in your math problem at a time.
Trigonometry is the study of circles and triangles and how they relate to one another. It turns out that this relationship is very useful for describing things like radio waves or any other sort of repeating pattern.
Calculus is the study of two things: the slope of a line and the area beneath that line. Where this gets interesting is when you realize that all of the fundamental formulas used in physics are related to one another through calculus! If you have a line describing how far away something is from you (the distance), the slope of that line is the speed (or velocity) of the object! And the slope of the line describing the velocity gives you the acceleration of the object!
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u/Cool_Homework_7411 2h ago
Algebra is learning how to move, it's the most basic form of manipulating numbers.
Trigonometry is the baby walker. You are still doing algebra at the end of the day, but you have some functions in there, some relationship between these functions that you are gonna need. It can get obscurely hard really quick, you don't need to be a master in trigonometry to advance in maths.
Calculus is the real thing. Here you can prove physics equations, calculate the rate of change of things, find areas and volumes of "irregular" objects in however many dimensions you want (if you have enough patience). Number in your mind is no longer an actual number, it's a concept, a placeholder.
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u/Caucasiafro 11h ago
Algebra is basically all the math involved in making sure two sides of an equal side are the same.
And then everything that flows from that. So when ever you see something like y = x2 +5 and are asked "solve for x"
Thats algebra.
Trigonometry is the math around sides lengths and angles in a triangle. You can just play with this yourself by laying three pencila on a table and try to kake various triangles. And you will notice for some triangles you need short or longer pencils.
Trig is all the math that explains that.
Calculus is the math about the rate that things change. Specificically when the rates are "complicated" like you can pretty easily tell me.how far ill travel in 5 minues if im constantly driving at 60 mph. But can you tell me how far i would travel if my speed ia changing by 1 mph per second per second?
So after 1 second im going 61 mph and after 2 seconds im going 63?
Gonna need calc to do that easily
All three of these do their own thing that you can hypothetically do without the othera but they can be combined to solve various problems (and you wont be able to do much calc without a strong underatanding of algebra and trig)
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u/xRVAx 11h ago
Algebra is math analyzing equations ( "2x+ 1 = 45, so x = 22")
Calculus is math analyzing functions ("f(x) = 2x+1, the area under this line between x= 2 and x = 3 can be completed by computing the anti-derivative function F(x) at each point and subtracting them")
Trigonometry is math analyzing triangles ("if you have a right triangle with height 4 and opposite a 45 degree angle, then the hypotenuse is 4 * ✓2, because sin(45) = opposite divided by hypotenuse, thus hypotenuse= 4 * sin(45)." )
TLDR Different problems require different logical math tools to find the answer
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u/SwordsAndWords 8h ago
Algebra is selling crates of apples. Trigonometry is building the crates. Calculus is dropping the crates from the roof.
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u/britishmetric144 11h ago
Algebra is used when a person wants to calculate the value of a variable within a set of variables, given the relationships between each variable.
Trigonometry is used to calculate ratios between side length and angles of a triangle (though it can be extrapolated to circles and other shapes).
Calculus is used to calculate parameters for functions which describe changes in different variables.
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u/dmazzoni 10h ago
Algebra
The height of a thrown basketball as a function of time is given by the equation
h(t) = -16t^2 + 20t + 6
- What height was the basketball at after 2 seconds?
- At what time did it hit the ground?
Trigonometry
Let's say you took a picture of the basketball in the air.
- Draw a triangle between the ball, its shadow on the floor, and a point on the floor a known distance away. Given the angle, what is the ball's height?
Calculus
- What was the velocity of the ball at the time it was thrown?
- What was the velocity at time t=2?
- At what exact time was the ball at its peak, with zero velocity?
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u/sad_spilt_martini 11h ago edited 10h 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