The right way to learn high school math.

[dragon513]

Hi, I'm a grade 12 high school student in Canada. This semester I'm taking math, chemistry, and physics and I've been really enjoying these classes so far. However, one question I can't even dare to ask my teachers is that why we are expected to memorize all those formula/equations. (ex/ Trig. Identities, Centripetal acceleration.) My math class is on Trig. and today my teacher gave us a sheet of paper which was full of equations (A Summary of Basic Identities and Formulae) and told us to memorize half of the stuff. So at home I started doing the h/w. I wrote down the identities repeatedly on a sheet of paper. However, I wanted to know how/why those identities work. So I went on Google and did a quick search. This http://oakroadsystems.com/twt/pythag.htm#squaredTop" came up and 5 minute of reading it saved me from 30 minute + of repetitive memorization. So I was wondering why the teachers wouldn't show us how those stuff(ie trig. identities) were derived at the first place. Surely deriving trig. identities weren't hard at all. Maybe they are just too lazy -_-??

 

[mattmns]

The problem is that half of the students would probably be confused, so your teacher, and other teachers, just think it easier to ask their students to just memorize some formulas. If you can derive the formulas yourself, great, I would continue to do that as you have a better understanding of how things work.

 

[DeadWolfe]

Students would be confused by division? Dear God...

 

[Poop-Loops]

Just do what I did: Never learn trig by playing games on your calculator the whole year and jump into Calculus.

I am taking multivariable calc and I STILL don't know 75% of those trig identities. I only know the most basic ones. If I ever see some nasty trig, I'll just whip out my nifty formula sheet I got with my book, or google it. Bam, problem solved.

The real problem is that nobody ever tells you what trig is until you get to calc. You get the formula sheet like in your class, ask "what the hell does this mean?", but don't find out until much later that it's ALL about triangles.

PL

 

[CrusaderSean]

I didn't take a proper precalc class in high school thus I never memorized any trig identities (well I know basic ones but not half or double angle). You need to know basic trig identities in calculus, but your professor should tell you. Otherwise in electrical engineering classes, we usually convert to complex exponential to avoid messy algebra with sine/cosine.

edit: I guess I'm not being very specific. Rather than telling you which formula to memorize, I think it's better for you to understand how sin/cos/tan (and their inverses) behave and look like and maybe sinh and cosh. I've never been stumped by a problem because of trig identity.

 

[jtbell]

My philosophy is not to bother specifically memorizing formulas like trig identities. Instead, I tell my students to be aware of what kinds of identities exist, and look up the exact formulas in a table or crib sheet when necessary.
For example, I don't try keep straight in my memory all the formulas for sine and cosine of a sum or difference of angle. But I do know what they look like in general, so if I see something like $sin \alpha cos \beta + sin \beta cos \alpha$, I can say "aha, that looks like one of those identities," and look up which one I want.
You'll use certain identities more often than others, and memorize them naturally. For example, in physics you use $\sin^2 \theta + \cos^2 \theta = 1$ so often, that pretty quickly you won't need to look it up any more.

On the physics side, I think it's important to memorize formulas that are definitions of some quantity, for example kinetic energy, momentum, work, etc.; but not "derived" equations like the range of a projectile.

 

[leon1127]

During the test, memorisation is better than you derive it during the test.
I never memorised a single formula and i derive it during the test (well, i know the basic formula to start with) it took way to long to do it.

 

[shmoe]

Expectations of students are going down all the time. I remember going through derivations of many trig identities in high school (also Canada). Unfortunately the voices demanding kids do well in school are sometimes louder than the voices demanding the kids learn something, so material is often dumbed down.

Kudos to dragon for seeking out futhur explanation of the material rather than rote memorization. It will do you well in the long run. Keep it up!

 

[moose]

Students would be confused by division? Dear God...

It's true... This exact scenario occurred a few days ago in my Precalculus class

It's sad really...

 

[dragon513]

Thank you all for your great responses.
You helped me setting my study direction

 

[michealsmith]

i think u need them learn them (memorized them in a sense -but from useing them) , because u'll need to use them but for a deeper understanding u need to be able to derive them and even understand where they came from (not all of them).

 

[Zarathustra1]

I remember learning about the Fundamental Theorem of Algebra in Precalculus, and, much to my frustration, they did not provide the proof for it because it was above the precalculus level. I would imagine that this situation is quite common in high school math, and sometimes you might have to live with it.

Personally, I like to both understand the derivations and memorize the formulas. Why, mathematic concepts are only interesting to me if I understand why and how they work.