Is Algebra and Trigonometry: Structure and Method Enough for Higher Maths?

[Daniel Y.]

Hello f(r)iends! The book I've been using for my Algebra II class is Algebra and Trigonometry: Structure and Method, and I've been doing every single exercise/problem in it for every topic, and it seems to be a sufficient resource for Algebra to prepare me for higher maths (correct me if I'm wrong). But I'm a little concerned about the and Trigonometry part of the book. Here's a full list of the topics covered in the book:

http://nutshellmath.com/textbooks_glossary_demos/textbook_content/alg2_and_trig_struct_method.html"

Do you think it's sufficient to teach me what I need to know about Trig? I've seen 5" thick books just on Trigonometry, and this seems to put it on the back end of Algebra (covers Analytic Geometry, too). Should I just get a full-blown Trigonometry text and use that instead? Or will this do the trick? Any help is much appreciated, thanks!

- Concerned high school student

 

[mgiddy911]

There are nearly endless algebra and trig "tricks" to learn. You WILL use them in higher maths however that does not at all mean you can't succeed without knowing them before hand ( I rarely did ).
Don't go overboard on trying to memorize every single algebra and trig identity.

For first year college physics and calculus just a working knowledge of algebra and trig is needed. If you pass your high school classes reasonably well then you should be fine. If you really have been doing every problem in your book I think you are more than ready for higher maths once you are finished.

 

[Feldoh]

Trigonometric Functions in Triangles
Radians, Cofunctions, and Problem Solving
Graphs of Trigonometric Functions
Trigonometric Function Relationships
Algebraic Manipulations
Sum and Difference Identities
Double-Angle and Half-Angle Identities
Proving Identities
Inverses of Trigonometric Functions
Trigonometric Equations
Right Triangles and Problem Solving
The Law of Sines and the Law of Cosines
Trigonometric Notation for Complex Numbers

This are the main points to cover in all the pre-calc/algebra II courses I've seen here in the US. About the only thing it doesn't really seem to cover are those really obscure trig identities

 

[rocomath]

Precalculus: Unit Circle Trigonometry by Cohen is pretty good. He has the best problems from what I've seen.

 

[Daniel Y.]

So anything else that isn't covered in this (or most) books before Calculus I will usually acquire as I move along through Calc and shouldn't worry about it. Also, does this seem like a good introductory Calculus text?

https://www.amazon.com/gp/product/0618239723/?tag=pfamazon01-20

I figured I might pick it up while I still can. It seems to be the preferred book for first level Calculus (over Stewart for example). And seeing as it's only $20 (used)...

 

[mgiddy911]

So anything else that isn't covered in this (or most) books before Calculus I will usually acquire as I move along through Calc and shouldn't worry about it. Also, does this seem like a good introductory Calculus text?

https://www.amazon.com/gp/product/0618239723/?tag=pfamazon01-20

I figured I might pick it up while I still can. It seems to be the preferred book for first level Calculus (over Stewart for example). And seeing as it's only $20 (used)...

As for picking up the rest as you go along, Yes that should be how it works. In calc class in college your professor may go from one step to another while making a comment along the lines of " now I'm sure you all remember 'x' identity or property from algebra" then he will perform the trick and show it to you and chances are he probably doesn't really expect that you all knew it.

As for that book, It seems good. It looks similar to the one I used in high school senior year for AP calculus, ( 2 years ago) and thus yes I would think it is a good introduction. It probably is not as rigorous as Stewart or Apostol and thus is a good intro especially for self study.

 

[ice109]

no one expects you to remember almost any of those trivial things

 

[zhentil]

I teach my students three trig identities. sin^2 + cos^2 = 1, cos(x+y), sin(x+y). If you know these, along with the definitions of the other trig functions, you'll be fine. I would strongly recommend you learn trigonometry in relation to the unit circle. I'm surprised by just how many professors even struggle to remember stuff like cos(x+Pi), which is trivial if you have the unit circle in your mind at all times.