Trig

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CalebC
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Trig

Postby CalebC » Thu May 13, 2010 10:19 pm UTC

My math teacher has made the offer that if I can get an %85 on the precalc final that I can skip straight to AP calc next year, but I don't know much about trig. If anyone could sort of explain everything there is to be known on the subject, that'd be pretty sweet.

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Yakk
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Re: Trig

Postby Yakk » Thu May 13, 2010 10:27 pm UTC

SOA CAH TOA?

Cosine law.

SEC, CSC and COT.

Symmetry.

pi/2, pi/3 and pi/6.

Double-angle and sum formulas.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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squareroot1
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Re: Trig

Postby squareroot1 » Fri May 14, 2010 12:05 am UTC

In an approximate order (may overlap with other posts.)

Definitions of sin, cos, tan, and their reciprocals and inverses including domains and ranges.
Unit circle and periodicity.
Symmetries and translations of sin, cos, and tan.
Radian angular measure.
Sine and cosine laws for triangles.
Values for special angles (0º, 30º, 45º, 60º, 90º).
Sum, difference, double and half angle formulas.
Pythagorean trigonometric identity.
Formulas for standing and traveling waves. (Amplitude, phase, velocity.)
Complex numbers (if you don't already know them.)
Polar form for complex numbers.
De Moivre's formula.
Roots of unity.

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jestingrabbit
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Re: Trig

Postby jestingrabbit » Fri May 14, 2010 12:51 am UTC

Yakk wrote:SOH CAH TOA


ftfy
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Tirian
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Re: Trig

Postby Tirian » Fri May 14, 2010 1:55 am UTC

jestingrabbit wrote:
Yakk wrote:SOH CAH TOA


ftfy


Some Old Horse Caught Another Horse Taking Oats Away

(Or the same with hippies and opium if you prefer the edginess of 70's mnemonics instead of the wholesome ones from the 50's.)

Honestly, I'd go to the library or bookstore and get a precalc review book and speed-read it. Actually, DO buy it, because you'll want a reference book handy when you move up to AP Calc. I think it's achievable, but all of the identities and stuff are probably more than you'll be able to pick up in a single forum thread.

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squareroot1
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Re: Trig

Postby squareroot1 » Fri May 14, 2010 2:59 am UTC

Actually, all of the various trig identities are derivable using the Pythagorean identity and the angle sum formulas.

Alternatively, everything can be derived through creative use of the Euler formula (but I don't think it is traditionally covered in Trig.)

The tangent of the half angle method is also rather useful for proving identities.

CalebC
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Re: Trig

Postby CalebC » Sat May 15, 2010 4:26 pm UTC

Tirian wrote:(Or the same with hippies and opium if you prefer the edginess of 70's mnemonics instead of the wholesome ones from the 50's.)


Groovy. Thanks for the help guys. This mnemonic device made my day.

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the tree
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Re: Trig

Postby the tree » Sun May 16, 2010 3:36 pm UTC

I was taught it as "Some Old Hag Cut All Her Teeth On Apples".
CalebC wrote: If anyone could sort of explain everything there is to be known on the subject, that'd be pretty sweet.
The thing is, that's kind of a lot and we don't know your specific syllabus. Without knowing where to stop we could either give you way too much information (you probably really don't need to know about complex numbers or anything following that) or way too little (do you need to know sum and difference formulae? I don't know).

Your best bet is to get hold of some example questions that represent what will appear on the test (past test papers are the best thing for cramming) - if you know how to do a question then work through it. If you don't, then ask us. We work better with specific questions than vague and open ones.

Thisisnotasmile
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Re: Trig

Postby Thisisnotasmile » Sun May 16, 2010 4:37 pm UTC

Sex On Hard Concrete Always Hurts The Other's Ass

clearly wins.

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Kurushimi
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Re: Trig

Postby Kurushimi » Sun May 16, 2010 4:56 pm UTC

The trigonometric functions and what they represent.
The trigonometric identities.
The trigonometric sum / difference formulas. (and the double and half angle formulas derived from them).
And, I think you'll also need to know how to represent a complex number with an angle / radius and trig functions. And be able to multiply and divide complex numbers of this form. And be able to find the nth root of a complex number written in this form.

That's what I needed for trig. I suppose there may or may not be more things, but these would just be using these things and have them applied to different scenarios. This is the basis of all you need to know.

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Eebster the Great
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Re: Trig

Postby Eebster the Great » Mon May 17, 2010 6:20 am UTC

squareroot1 wrote:In an approximate order (may overlap with other posts.) . . .
Formulas for standing and traveling waves. (Amplitude, phase, velocity.)
Complex numbers (if you don't already know them.)
Polar form for complex numbers.
De Moivre's formula.
Roots of unity.

Most precalc classes probably won't cover all of these, but it depends. The wave formulas in particular are more likely to show up in a physics course, and the complex numbers are not necessary for any part of the AP Calc BC curriculum, although they are important to know later (and not that hard).

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squareroot1
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Re: Trig

Postby squareroot1 » Mon May 17, 2010 9:07 am UTC

Well, wave motion is kind of the example for what trig functions actually get used for, but whether they would get covered in a particular trig book is questionable.

I have to admit I have a soft spot for complex numbers (mainly because they make everything else so easy). But they ended up that far down the list precisely because they would be covered later (if at all.)

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Eebster the Great
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Re: Trig

Postby Eebster the Great » Tue May 18, 2010 12:06 am UTC

squareroot1 wrote:Well, wave motion is kind of the example for what trig functions actually get used for, but whether they would get covered in a particular trig book is questionable.

I would argue that right triangles would be the example. And you know, finding distances and stuff.

But yeah, I get your point. Waves and SHM are probably the best examples, especially if you don't yet know any calc or complex numbers.

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lu6cifer
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Re: Trig

Postby lu6cifer » Tue May 18, 2010 12:41 am UTC

Pick up a barron's SAT II Math book and make sure you know everything on there.
(Aside from matrices and vectors and shit...at least, those aren't covered in our curriculum)
lu6cifer wrote:"Derive" in place of "differentiate" is even worse.

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Eebster the Great
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Re: Trig

Postby Eebster the Great » Tue May 18, 2010 4:15 am UTC

lu6cifer wrote:(Aside from matrices and vectors and shit...at least, those aren't covered in our curriculum)

While not strictly necessary for single variable calc, these are pretty important to know, in general. I would argue they are more important than calculus, in fact.

(They are more important than partial fractionation, anyway.)


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