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Trig identities
Fizban140
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Registered User, __BANNED USERS regular
I have a trig final on tuesday and I can't figure out identities. Like figuring out what tanx/2 is equal to or any of it except cos A+/-B and sin A+\-B. I obviously know all the easy shit like sin^2+cos^2 = 1 and all of those but I just can't do these massive algebraic conversions. For example
I am trying to prove that (sin^2x)/2-2cosx = cos^2 x/2 and I get to a point where I have 1-cos^2\2(1-cosx) = cos^2 x/2 which I can cancel out to be 1+cosx/2 = cos^2 x/2
I don't get how those equal eachother, it doesn't make sense to me that a function squarerd and divided by two could equal a function plus 1 and divided by two.
I am trying to prove that (sin^2x)/2-2cosx = cos^2 x/2 and I get to a point where I have 1-cos^2\2(1-cosx) = cos^2 x/2 which I can cancel out to be 1+cosx/2 = cos^2 x/2
I don't get how those equal eachother, it doesn't make sense to me that a function squarerd and divided by two could equal a function plus 1 and divided by two.
Fizban140 on
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I'm not sure I totally follow the way you're writing these equations, but I understand that to complete your proof, you need to prove that [cos(2x) +1]/2 = (cos x)^2 ?
Start with the identity for cos(A +
The expression you will obtain will link cos2x to (cos x)^2 and (sin x)^2. From this, you can use (cos x)^2 + (sin x)^2 = 1 to convert your expression in terms of cosines.
I know that sin2a is equal to sin(A+A) so sinAcosA+cosAsinA = 2sinAcosA is that correct? So now to find sinA/2 what do I do? if I know that sin2a=2SinAcosA then where do I go? I have no idea how to even begin.
cos (x/2) = ((1+cos(x))/2)^.5
so cos^2(x/2) = (1+cos(x))/2
or were you looking for a proof?
I didn't happen to have the half angle formula for cosine floating around my head, I looked it up.
is there some reason you'll have to do trig transformations a year from now?
Seriously. You don't have to know why right now. You just have to know that it works and remember it so you can use it. And depending on the kind and level of Calc you take, you won't even need to know it then.
What do I need to learn for calculus? I plan on making use of my time off.
But get used to just memorizing formulae - especially the trig stuff. For Calc I for majors (which you will probably have to take) you're going to have to do more than memorize a list of trig identities... you're going to have to memorize pages and pages of their derivatives, too. My teacher didn't make us memorize them, he just gave us pages and pages of formulae to use and said "know how to recognize and apply these". I know other teachers in the department wanted their students to remember them all, so I consider myself lucky.
You are going to have to get used to memorizing shit you don't know what it means and will only learn later, MAYBE.
most likely, they will not involve trig identities, just the regular sin, cos, tan, cot, sec, csc.
when you learn the chain rule they might do trig identities but not in the way that you'll have to know what cos(x/2) is transformed into.
Trig identities too. I have forgotten all but a few (but they do come in handy), so when I need them I look them up. If you are in a trig class though, you absolutely need to memorize them, because that's the whole point of your class.
All in all I echo cere's advice, take precalc before jumping into calculus. As an engineer I took precalc before calc and it was a wise choice. It gets you back into the swing of things, you learn fundamentally what a function is as well as a somewhat thorough review of trig, algebra 2 (solving systems of equations) and all that jazz.
Get used to memorizing though. It's not all that bad, it's not like biology or something. The interesting thing about mathematics is that the shit you memorize and apply now can be used throughout your entire career (at least as an engineer).
but my personal experience is that precalc was a waste of time.
I suggest trying out calc 1 and for a few weeks and talk to the professor when you start, if you're doing badly or aren't confident then I suggest dropping the class and trying to get into a precalc class.
if you want to study up before hand, go with
geometry: area, surface area and volume of basic shapes, graphing
algebra: fractions, solving equations, basic trig functions, multivariable equations
other areas to look into: sequences and series, limits
Also, as a general rule, taking math over the summer short sessions is a Bad Idea unless you're just brushing up - the classes are compressed into a much shorter time span and you definitely don't learn as much as you would during a full semester.
As for the final, you might want to corner your TA/GSI and ask for some help, as that's one of the reasons that they're there. But yes, trig identities and geometry formulae are just there for you to memorize right now, you don't need to worry about the why until Calc II/III.
Mathematicians can do many proofs with just a piece of paper and a pen, not because they've got thousands of proofs memorized in their heads, but because they have developed a way of thinking that allows them to figure out how to do those proofs.
They start with what they know, and keeping the goal in mind, they work their way through a proof. They'll try a bunch of stuff that doesn't work, or make mistakes along the way, but they'll eventually find the right way.
I didn't have to look up anything to make my post because I knew what I wanted to prove and had memorized a few basic trig facts (then again, it wasn't a very complicated proof, but the same principles apply). So you do need to memorize a few things, but it really is not as bad as you think. You are of course more efficient if you remember more things, but many things can be done with just a few hazy memories and something to write on.
At any rate, as an engineer, you won't have to do super complex mathematical proofs as part of your job. Just make sure that you know where your mathematical knowledge comes from, so that you know what to use as a reference.
Edit: Also it's been years since I took Calc 1 but I don't recall much if any trig. Calculus is more about limits and series.
But also I have a final on tuesday.
As for Pre-Cal, I suppose its good to see all the material again - but you are correct in thinking it is nothing but a review of the material you've covered already, and an introduction to material you will cover again. The insane thing about Pre-Cal is that the teacher will come at the material assuming you HAVENT seen it before. So is Pre-Cal an absolute pre-req for Calc 1 - no, especially if you are not required to take. Will it hurt - of course not. However if your math game is good and you can run through a Pre-Cal book (at least the first 2/3's) you should be ok.
Not because it isn't repetition, but because it is very, very clear that you NEED the repetition in order to be successful with this. There's no shame in this.
Maybe find out what textbook they use? Because my Calc I class was like 5 solid weeks of trig crap and its derivations. I had a pretty tough time with limits, too, but that they don't touch in precalc.
Personally I was never able to learn shit just from a textbook, I needed someone to do it in front of me, but others may learn differently. I think there are two kinds of things you learn in math - things you learn because you need to know them to do later stuff, and things you learn because there is a test next week. I think trig identities are the latter, especially for an engineering student who will be spending a lot of time with a calculator in hand once they get in-program. I would much rather have a rigorous understanding of limits and series. I only really used trig identities when I got to advanced calc and you are expected to switch between cartesian and polar coordinates every 5 minutes.