Some questions about trigonometry

[awholenumber]

Does these two picture cover everything about trigonometry ?
Is anything important missing ?

 

[jedishrfu]

For a first course in it, it does but as you get into Calculus and beyond then there's more to learn:
- the series approximations for the trig functions
- the derivatives and integrals of trigonometric functions
- the use of trigonometry in vector calculus, real analysis and complex analysis
- the use of trigonometry in coordinate systems and rotational transformations
- the use of trigonometry in Differential Equations
...

 

[awholenumber]

Thanks jedishrfu ,


This may look a bit stupid , but i have been trying to learn calculus from scratch ,
I have been refreshing my

Arithmetic
Algebra
Trigonometry

like this ...

whole numbers , natural numbers , integers , rational numbers , irrational numbers .

factors ( reducible), prime factors (irreducible), greatest common factor (same as greatest common divisor ), least common multiple

Monomial , binomial , trinomial , polynomial

simplify , factoring (factorization )

Factoring polynomials

’To factor’ means to break up into multiples.

Methods of Factoring

Factor by Distributive law method

Factor by grouping

Factor by Splitting

Factor by Very Famous Polynomials

Then after that you learn trigonometry ,

One more question , What do i learn after this ?

I am trying to learn calculus ...

 

[jedishrfu]

Take a look at the website mathispower4u.com there's a whole collection of videos on these very topics that you can browse.

The list alone will give you an idea of what to cover.

In general:
- algebra
- geometry
- trigonometry
- precalculus: series, sequences, probability, complex numbers...

Their algebra2 and trigonometry video lists covers the last two above:

http://www.mathispower4u.com/alg-2.php
http://www.mathispower4u.com/trigonometry.php

But I would encourage you to look at the algebra-1 and geometry ones as well to see if you missed anything.

There's also the Khan Academy videos if you don't like the mathispower4u format.

You can also start to dabble in Calculus, I did that learning the operational aspects like differentiating a function and integrating one but it helps if you have a good foundation to start with. I was weak on limit theory and proofs but for a physics major, I learned what I needed to learn to use Calculus.

The culmination of all this study is Vector Calculus which incorporates nearly everything you've learned up to this point. Then you can begin to understand Electromagnetism and get to do some interesting problems.

 

[awholenumber]

Hey jedishrfu , Look what i just found , i can't believe it , its like hitting a gold mine of information or something like that ...omg , i feel so excited and happy ...

:)

 

[awholenumber]

Just a bit of an update , let me try to put all the things i have learned or trying to learn in one post ...

Ok so it starts with


Arithmetic
Algebra
Trigonometry

whole numbers , natural numbers , integers , rational numbers , irrational numbers .

factors ( reducible), prime factors (irreducible), greatest common factor (same as greatest common divisor ), least common multiple

Monomial , binomial , trinomial , polynomial

simplify , factoring (factorization )

Factoring polynomials

’To factor’ means to break up into multiples.

Methods of Factoring

Factor by Distributive law method

Factor by grouping

Factor by Splitting

Factor by Very Famous Polynomials

After that trigonometry ,

Calculus Derivatives and Limits

Calculus Integrals

The only thing missing from this awesome looking list of information is differential equations ,This is sweet :)

 

[UsableThought]

This may look a bit stupid , but i have been trying to learn calculus from scratch ,
I have been refreshing my
Arithmetic
Algebra
Trigonometry
like this ...

Have you looked into ALEKS? It's an automated system for drilling and testing on math subjects.
Web site here: https://www.aleks.com
"About" page here: https://www.aleks.com/about_aleks

It's often recommended here by @Dr. Courtney, a researcher & educator who belongs to the forum; here are search results you can look through to read why he recommends it: https://www.physicsforums.com/search/5157867/?q=ALEKS&o=relevance&c[user][0]=117790

Personally, I've investigated it enough (including a short trial) that I'm pretty confident it will be helpful for my own math self-study, including many of the topics you list. A subscription is roughly $20/month. The advantage is that it tests you (fairly cleverly) to see what topics and sub-topics you're weak in, so you know where you have gaps and can concentrate on those.

With me, for example, I am working with 3 different high school-level algebra books (Gelfand; Brown et al; and Axler). I am doing this because each book has different strengths, e.g. Gelfand is fun but doesn't cover all topics in depth; and Brown is at a more elementary level than Axler. However this approach means there's a potential for gaps as I move from one book to another; and so ALEKS will help me make sure I don't miss anything when I do this.

 

[Dr. Courtney]

There are often trade-offs between mechanical skills, deeper understanding, and broad coverage.

I've seen so many students flunk out of college or change from STEM majors due to skills weaknesses, that I favor a skills-based approach that allows broader coverage and deeper understanding to come later. Few STEM majors realize, that 90% if the trig most often used in intro physics and engineering courses is SOHCAHTOA.

ALEKS is a nice balance, and it quickly focuses on what you need to practice without excess repetition in areas where a student is already strong. It slices the time pie very well, optimizing skills improvement for a give investment in time and effort.

It is always tough to look at any list and say, "That's all (100%) you need to know."

But ALEKS pre-calc is at least 90% of the high school math you need to know for most first year STEM courses in college.

 

[awholenumber]

UsableThought , Dr. Courtney

Thanks for that ALEKS Link ,i will look into it, when i have enough time

What do you guys think of that post #6 ? I updated it a bit :)

I wish i could find a list like that for differential equation too

 

[Mark44]

Just a bit of an update , let me try to put all the things i have learned or trying to learn in one post ...

Please stop doing this!
The fact that you have found a number of web pages with this information means very close to nothing, in light of your recent posts about factoring. Finding an image on the web and understanding what is on the image are two different things.

Ok so it starts with


Arithmetic
Algebra
Trigonometry

whole numbers , natural numbers , integers , rational numbers , irrational numbers .

factors ( reducible), prime factors (irreducible), greatest common factor (same as greatest common divisor ), least common multiple

Monomial , binomial , trinomial , polynomial

simplify , factoring (factorization )

View attachment 196919


Factoring polynomials

’To factor’ means to break up into multiples.

Methods of Factoring

Factor by Distributive law method

View attachment 196920

Factor by grouping

View attachment 196921

Factor by Splitting

View attachment 196922
Factor by Very Famous Polynomials

View attachment 196923

View attachment 196924

View attachment 196925

After that trigonometry ,

View attachment 196926

View attachment 196927

Calculus Derivatives and Limits

View attachment 196928

Calculus Integrals

View attachment 196929



The only thing missing from this awesome looking list of information is differential equations ,This is sweet :)

I disagree. Without understanding, all you have done is compiled lists of a wide variety of techniques to do various things. What is your purpose with all these lists? Do you plan to rote memorize all of these formulas? This is not the way to really learn anything.

 

[Mark44]

What do you guys think of that post #6 ? I updated it a bit :)

Not much. All it shows is that you are able to copy and paste a bunch of images. That post doesn't tell me anything about your abilities to actually do anything.

I wish i could find a list like that for differential equation too

Why? Learning differential equations takes a lot more effort than merely compiling a list.

 

[awholenumber]

I am sorry about the images , i was trying to collect some really good materials on the subjects i was trying to learn .
Most of the local books lacks all these quality stuffs , all of those local texts only makes the learning process a bit harder
I am from India and i have to depend on the internet for some quality texts and study materials like these , which is why i was a bit excited to see a nice list of things i could follow .

 

[Mark44]

I am sorry about the images , i was trying to collect some really good materials on the subjects i was trying to learn .
Most of the local books lacks all these quality stuffs , all of those local texts only makes the learning process a bit harder
I am from India and i have to depend on the internet for some quality texts and study materials like these , which is why i was a bit excited to see a nice list of things i could follow .

Those images are useful reminders after you have learned the material, but when you're starting out, such summaries aren't useful at all, IMO.

If you want to learn trigonometry (which is the title of this thread), get a textbook and work through it. Here's a link to an amazon page listing a lot of different trig textbooks. I don't think you can go too far wrong with any of them. There are also websites, such as khanacademy.org, but having an actual textbook is advantageous, IMO, as you have a book that you can refer back to if you forget something.

Edit: Forgot to add the link before, so here it is: https://www.amazon.com/s/ref=nb_sb_ss_c_2_12?url=search-alias%3Dstripbooks&field-keywords=trigonometry&sprefix=trigonometry%2Caps%2C204&crid=11NTJNIR3N0Y0&tag=pfamazon01-20

 

[awholenumber]

Thanks for the suggestions Mark44 ,
At least now i know where to improve and what to follow , before i can start working with differential equations once again ...

This is where i should try to improve my mathematics , this is like the 5th round or something like that ...

Arithmetic
Algebra
Trigonometry
Differentiation
Integration

And finally differential equation , which i don't have any clue at all :)

Sorry for going off topic , the thread was about trigonometry :)

 

[UsableThought]

Finding an image on the web and understanding what is on the image are two different things.

I am from India and i have to depend on the internet for some quality texts and study materials like these , which is why i was a bit excited to see a nice list of things i could follow .

I sympathize with the desire to collect a trove of useful-seeming information in advance of studying a subject. In my case, living in the U.S. with ready access to Amazon and big brown delivery trucks, I have a rather obsessive tendency to try and find "the perfect algebra book," for example. To paraphrase @Mark44, there is a big difference between searching for and acquiring books on math, and actually reading & understanding even just a single page of one of those books!

Fortunately I find that when I settle in and work on math, I enjoy it. Progress is slow, but fun. But basically I agree w/ Mark about the images you've posted: they look like convenient reminders after you've learned a topic, but I wouldn't use them to guide your learning, as they don't show hierarchical or conceptual relations between topics, recommended order of learning, necessary background knowledge, etc.