Thread: Lower Grade Level for Trig and Algebra ?

Hello, I need some resources or books that can teach Trigonometry and Algebra that relates to vectors, matrices etc at a lower grade level to understand the basics, before moving up the ladder, any online or book suggestions ?

Hey GreyWolf.

I don't know about any specific resources that meet that need, but one thing that you can do is discuss the rotation matrix. This will link all the topics together in a nice fashion.

The idea is that you start off in 2D and you want to rotate a point some angle. So you start with a point (x,y) rotate it (x',y') and then construct the matrix to take (x,y) to get (x',y') where (x,y) = x, (x',y') = b and Ax = b where A is a 2x2 matrix.

You can derive this using some basic trig addition laws for sin(a+b) and cos(a+b) which can be proved either geometrically or otherwise. Once you do this you derive your rotation matrix and then introduce matrix multiplication where Ax = b and you can look at the inverse process to get x given b by using x = inv(A)*b, and show that inv(A) simply rotates by the negative of the angle by showing that you get -theta instead of +theta.

That should link up matrices, vectors and trig nicely.

Originally Posted by chiro

Hey GreyWolf.

I don't know about any specific resources that meet that need, but one thing that you can do is discuss the rotation matrix. This will link all the topics together in a nice fashion.

The idea is that you start off in 2D and you want to rotate a point some angle. So you start with a point (x,y) rotate it (x',y') and then construct the matrix to take (x,y) to get (x',y') where (x,y) = x, (x',y') = b and Ax = b where A is a 2x2 matrix.

You can derive this using some basic trig addition laws for sin(a+b) and cos(a+b) which can be proved either geometrically or otherwise. Once you do this you derive your rotation matrix and then introduce matrix multiplication where Ax = b and you can look at the inverse process to get x given b by using x = inv(A)*b, and show that inv(A) simply rotates by the negative of the angle by showing that you get -theta instead of +theta.

That should link up matrices, vectors and trig nicely.

I don't understand I know vectors are rows and combined are matrices. I want to get a basic understand, I'm still not understanding What are dot products, etc

Originally Posted by GreyWolf

I don't understand I know vectors are rows and combined are matrices. I want to get a basic understand, I'm still not understanding What are dot products, etc

This is a great resource. It is relatively inexpensive. It requires no calculus.

Originally Posted by Plato

This is a great resource. It is relatively inexpensive. It requires no calculus.

Any other book that breaks Vectors, Matrices, Dot Products etc, down almost to laymen terms, then I can gradually go up from there ?

Originally Posted by GreyWolf

Any other book that breaks Vectors, Matrices, Dot Products etc, down almost to laymen terms, then I can gradually go up from there ?

Frankly, that response mystifies me. What does it mean?
You always must start at some level of mathematics understanding.
The reference I gave you assumes nothing beyond basic pre-calculus.
Look, the study of vectors is not for amateurs.
You really do need to know basic calculus.
However, this is another book. Look for a text by h.m. schey.

Originally Posted by Plato

Frankly, that response mystifies me. What does it mean?
You always must start at some level of mathematics understanding.
The reference I gave you assumes nothing beyond basic pre-calculus.
Look, the study of vectors is not for amateurs.
You really do need to know basic calculus.
However, this is another book. Look for a text by h.m. schey.

At what grade level is Algebra and Triganmonety taught ? I need something that gets the mind started, jumping into it too far, I won't learn, my focus is on vectors and trigonometry with 3D shapes ? I hope that helps, imagine if you will, you knew almost nothing or forgot alot of this stuff, you don't have a personal teacher, so you need a book to get the mind started, that is basic, that can break down how a vector works, how a matrices works, what is a dot product etc. Explaining all of this, without fancy equations, but simple ways to understand, from that point once ready I can move up the latter.