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Old 01-24-2018, 09:03 AM
 
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I have noticed that the courses that tend to be considered "prerequisites" for Trignonometry are mainly Arithmetic and Algebra;
however, wouldn't Geometry also be a fairly important prerequisite?
The way I look at it, the most logical order to study fundamental math is this:

Arithmetic - (absolutely essential for Algebra and basically everything else, enough said)
Algebra - (necessary for being able to work with equations in Geometry)
Geometry - (useful for developing an intuition for geometric figures in Trigonometry)
Trigonometry - (useful for matrix rotation in Linear Algebra)
Linear Algebra - (useful for computing the Wronskian and the Hessian matrices in Calculus)

...which would then be followed by Calculus, possibly with a sidestep into Probability & Statistics.
The reason why I feel that Geometry seems like a prerequisite for Trigonometry is probably fairly obvious:
in Trigonometry you deal a lot with geometric figures, not only triangles but also circles (unit circle), and also to some degree parallelograms - at least when you do geometric additions of vectors in two dimensions, which is sometimes simpler than Cartesian addition.
So wouldn't it be strongly recommended to have a solid understanding for Geometry before jumping into Trigonometry?

I am already familiar with all of these courses and actually have some background in linear analysis and Fourier/Laplace Transforms, so I am asking you out of pure curiosity.
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Old 01-24-2018, 09:10 AM
 
Location: God's Gift to Mankind for flying anything
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Quote:
Originally Posted by Markus86 View Post
I have noticed that the courses that tend to be considered "prerequisites" for Trignonometry are mainly Arithmetic and Algebra;
however, wouldn't Geometry also be a fairly important prerequisite?
You do say "mainly Arithmetic and Algebra"

What were the other prerequisites ?

Last edited by irman; 01-24-2018 at 09:32 AM..
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Old 01-24-2018, 09:26 AM
 
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Quote:
Originally Posted by irman View Post
You do say "mainly Arithmetic and Algebra"

What are the other prerequisites ?
I meant that Arithmetic and Algebra seem to be the courses that are mentioned as actual prerequisites, whereas Geometry might sometimes be considered a "recommended preparation".

Personally I feel that it makes sense to start with Geometry before taking on Trigonometry;
I am not sure how "important" it is for that specific course, but you will definitely deal with a lot of geomtry in later courses, and Trigonometry seems to be the first course where Geometry will actually be relevant.
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Old 01-24-2018, 09:35 AM
 
Location: God's Gift to Mankind for flying anything
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Quote:
Originally Posted by Markus86 View Post
I meant that Arithmetic and Algebra seem to be the courses that are mentioned as actual prerequisites, whereas Geometry might sometimes be considered a "recommended preparation".
I agree with you !

I do not think you can learn trig by starting with trig, and NOT have any notion what Geometry is all about ?
The notations alone would spin your head, no ?
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Old 01-25-2018, 09:45 AM
 
Location: Rathdrum, ID
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Things have changed since I was in school, (70s). At that time, the progression of math courses was: Algebra, Geometry, Trigonometry, Calculus, then Linear Algebra. (This was the math component of a Computer Science major at a CA state university.)
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Old 01-25-2018, 09:55 AM
 
Location: Richardson, TX
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My high school track in the 90's was Algebra-Geometry-Trigonometry-Calculus. Unfortunately, I'm a dunce at Geometry. I loved Algebra.

I recently considered whether I should get second bachelor's degree in Computer Science and the 6+ higher mathematics classes in the track cooled my jets considerably.
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Old 01-25-2018, 01:34 PM
 
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In my case:
Middle School/HS:

Alg. 1 - 8
Geo - 9
Alg 2 - 10
Pre-Calc (including non-calculus based trigonometry) - 11
Calculus (including calculus-based trig) - 12

University:

Calculus 1A & 1B
Differential Equations 2A
Numerical Methods 2A
Vector Calculus 2B
Partial Diff. Eq 3A
Multivariable Calc. 3B

This for Mechanical Engineering.

I might have left something out, it was over 30 years ago.

Anyway, geometry has meaning not only as a prerequisite for trigonometry but as a prerequisite for many following areas of math study. Just as the crudest example, it's got to be a lot harder to understand the unit circle, the various trigonometric identities, the derivatives and integrals of trig functions, and so on, if you have never had plane geometry. When you get to non-plane geometry, conic sections, etc., etc., everything you do is shot through with basic geometry.

You know, people have been teaching mathematics the way it's done now for a very long time. Maybe there are reasons for that.
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Old 01-25-2018, 03:24 PM
 
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Geometry was an interesting course. The teacher told us that even though things weren't making sense that we should just keep studying. At some point the light bulb would go on and it would all make sense.

It did.

And Trigonometry was a class I didn't take in high school. Later I was hired to do drafting (before calculators) and the first week I was asked about how much I knew regarding trig. The engineer just rolled his eyes when I said, "Nothing", and mumbled something about the idiot in HR, lol.

So I went out Friday after work and bought a book called "Plane and Spherical Trigonometry" that had quizzes at the end of the chapters and answers in the back. I taught myself trig over the weekend, went in Monday and told the engineer I was set to go. That got a good laugh so I told him to give me some problems to solve, which he did. And I did.

That was in the mid 70's. The book is still available. https://www.amazon.com/Plane-Spheric...l+trigonometry

Worked there for 22 years.

I highly recommend adding trig to your courses. It's a fun kinda math.
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Old 01-25-2018, 03:34 PM
 
Location: Heart of Dixie
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Geometry is important in that it provides a solid foundation in mathematical proofs.
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Old 01-28-2018, 07:03 AM
 
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Yeah, I guess Trigonometry could be tackled even without any prior knowledge of Geometry - just like you can probably grasp basic Linear Algebra mechanics when you are learning to solve systems of differential equations etc without necessarily taking a full Linear Algebra course - but a solid background in Geometry would certainly be a big advantage.

I always liked Multivariable Calculus a lot by the way, there is something very satisfying about working with 3-dimensional graphs and finding volumes under surfaces etc.
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