Trig...it hurts

[CommodoreFluffy]

Yeah...I'm here to share my Trig woes.

[Cobra_Ikari]

I don't really know what trig is. but I'm sure I can do it. Maybe? >.>

...what's the problem?

[Em Blackleaf]

I like Trig. Well, the trig I've done. Which it's kinda simple-ish? Well, I liked that. It's easy.

[CommodoreFluffy]

I love the idea of trig, it is fun. But the problems take so long to write out.

a sample would be 34^2=24^2+18^2-2(24)(18)cosI

and then with numerous fractioned, exponented, sined, cosined, and tangented lines of math following just to solve a single triangle.

[PhantomFox]

I'm supposedly a Math major, so perhaps I can dig through my memory and remember some trigonometry. I'm sure I can remember a few relevant theorems.

[ziratha]

Ah, the generalized equation for non right triangles... Hehehe. Have fun with that.

Your first assignment: What is the exact value of sin(15) ? How about
cos(3) ?

[RS14]

But the problems take so long to write out.

Often I'll switch to writing S and C for sine and cosine respectively. It's a bit easier to write s^2+c^2=1 or s 2θ = 2 s θ c θ. It is a bit more likely to confuse, but if you're doing some long manipulation, it's sometimes easier (though your teacher isn't likely to approve).

Now, with a computation like the one you gave, I say just plug it into a calculator. As long as you're sticking to triangle geometry, it's mostly just a matter of knowing which law corresponds to which sort of triangle. Remember: The Law of Cosines doesn't need any angles, while the Law of Sines needs at least one. The Law of Cosines needs at least two sides, while the Law of Sines needs at least one. Thus if you have Side-Side-Side (SSS), use Law of Cosines; if you have AAS, use the Law of Sines. Think about which equation you can plug known values into to leave only one unknown.

I will say that Identities always gave me trouble. I too often wind up converting to what I have to Sines and Cosines and manipulating those, rather than dredging my memory for identities like Cot^2(θ)+1==CSC^2(θ).

Good luck.

[The Extinguisher]

Aren't they the exact values themselves, ziratha. It's been a while since trig, but are they not irrational numbers?

[evnafets]

If you think its painful now, Wait until you mix trig with calculus and start differentiating and integrating with these little guys

[Edan]

Step 1) Read this (http://en.wikipedia.org/wiki/Differentiation_of_trigonometric_functions) and this. (http://en.wikipedia.org/wiki/List_of_integrals_of_trigonometric_functions)
Step 2) Head Asplode
Step 3) ????
Step 4) PROFIT!

Truth be told, trig isn't that bad, learning the rules is the hard part.

PS: A good calculator can be a lifesaver, it was for me.

[CommodoreFluffy]

it ain't bad, it's long, and repetitive.

[Exachix]

Trig is sort of fun <.<.

At least now I don't need to care about hyberbolic sine, cosine, tangent, etc.

And the differentials are not that bad.
Until we did FP2 and differentiated arcsine, and arctangent.

I find trig fun anyway. ;P.

[Nychta]

Those equations: are they as long as you've ever come across? Because if so.... uh... I don't think you and maths are going to get on very well in the future...

[valadil]

Trig is one of those things that's really cool if you understand it and really painful if you don't. You need to know what all those numbers and angles actually mean. Otherwise it's just pure memorization. I've used trig once since I was taught it 8 years ago. I still remember the concepts behind it and it still makes sense even though the formulas are long gone.

[Szilard]

I had a teeny bit of introduction Trig a month or two ago as part of my Geometry class, a ninth grade class, full of eighth graders, cause were that awesome.

[Dragonrider]

If you think its painful now, Wait until you mix trig with calculus and start differentiating and integrating with these little guys

I actually quite enjoy THAT. :smallamused:

Which is weird, cuz I've never been a math person. :smallconfused:

integral 2cos(2x)dx = sin2x

*blissful sigh*

*has just finished calculus and likes understanding*

[Player_Zero]

re^ix = r(cosx+isinx)
(cosx+isinx)^n = cosnx+isinnx
sinhx=0.5(e^x - e^-x)
coshx=0.5(e^x + e^-x)
d/dx sechx = -tanhxsechx
d/dx tanh(x/a) = 1/(a^2 - x^2)
Integral(tanhx) = ln|coshx|+c
...etc.

Good times.

Show that if x = 4sinh^2 A

Integral(root((x+4)/x))dx = Integral(8cosh^2 A)dA

Also:
Find lim x => 0 [{ln((1+e^x)/2) + ln(1-(x/2)}/(x-sinx)]
Do it.

Then differentiate x^x^x. Show your working...

Wait, trigonometry? Then make that x^x^x^sinx.

Maths, it's what's for dinner.

[Haruki-kun]

Trig was the second easiest out of the 6 math courses I took in High School, right after Algebra I.

All others, Algebra II, Analytic Geometry, Differential Calculus and (:smallfurious:) Integral Calculus, were horribly complicated next to Trigonometry........

[Cristo Meyers]

re^ix = r(cosx+isinx)
(cosx+isinx)^n = cosnx+isinnx
sinhx=0.5(e^x - e^-x)
coshx=0.5(e^x + e^-x)
d/dx sechx = -tanhxsechx
d/dx tanh(x/a) = 1/(a^2 - x^2)
Integral(tanhx) = ln|coshx|+c
...etc.

Good times.

Show that if x = 4sinh^2 A

Integral(root((x+4)/x))dx = Integral(8cosh^2 A)dA

Also:
Find lim x => 0 [{ln((1+e^x)/2) + ln(1-(x/2)}/(x-sinx)]
Do it.

Then differentiate x^x^x. Show your working...

Wait, trigonometry? Then make that x^x^x^sinx.

Maths, it's what's for dinner.

^See this? This is why I majored in English.

Jeez, my head just exploded trying to read that.

[Player_Zero]

^See this? This is why I majored in English.

Jeez, my head just exploded trying to read that.

The my work here is done.

Interestingly enough, that's the basic stuff you're looking at for the FP2 module of further maths. Advanced stuff would be a bit harder to comprehend.

Anyone here done STEP exams, by any chance?

[bosssmiley]

sin, cos and tan are good for you! Eat 'em all up, or you'll never develop impressive conic sections.

[Bag_of_Holding]

I absolutely loved calculus when I did it in high school. Trig? Not so much. For no apparent reason at all, trignometry was my second least favourite right after probability. Probability? Ewww :smallyuk:

[Player_Zero]

I absolutely loved calculus when I did it in high school. Trig? Not so much. For no apparent reason at all, trignometry was my second least favourite right after probability. Probability? Ewww :smallyuk:

STEP paper probability questions are usually on rather odd subjects. The last one I reviewed was about a counting camel. Wherein you have to calculate whether a camel was guessing the answer to a mathematical problem or answering it to the best of its knowledge. Turns out that it was guessing... And guessing pretty poorly at that. The last part was evaluating whether or not you needed a new camel, which you did since this one was rubbish at counting.

True story.

[OwlbearUltimate]

I personally love math. I have done some trig, all the sin, cos, tan, stuff. Long Equations ftw! :smallamused:

[JoshuaZ]

You need to study trig because otherwise you'll never understand why e^(i*pi)+1=0.

[SurlySeraph]

*whimpers quietly*

I was fine at trig up until we started doing things with circles. Triangles I can deal with. Circles I can't deal with as much.

And then there were cycloids. I understand absolutely nothing about cycloids, and I never did. But they've never been important, so that's OK.

And now we're doing calculus with trig functions. And the teacher expects us to remember all the triangle side-angle relationships that we learned in angles in radians. And finding the area between two trig functions is made out of pain and lose. And finding the volume of that area rotated around a line is even worse. And tomorrow I have a test on all the calculus we've learned this year, most of which I have forgotten. *clutches his knees to his chest, whimpers*

[Zarrexaij]

If you think its painful now, Wait until you mix trig with calculus and start differentiating and integrating with these little guysPfft, integrating and differentiating trig functions isn't that hard.

I absolutely loathed trig. I'm actually surprised I made an A in that class. Some of it made absolutely no sense to me, but then again it has more to do with algebra than geometry.

Then again, nothing in calculus is like "Me no gets!"

[CommodoreFluffy]

it's not any of that, it's just so simple for such a long equation. I really enjoy trying to find out stuff with long, complicated proofs and equations, It is fun, but trig is so simple for the amount of writing you have to put down. I'm one of those kids who doesn't show work, and now that I'm trying, the ratio of writing to mental process is 100/1costheta

[Dave Rapp]

YOU PEOPLE ARE SILLY.

YOUR MATHS ARE SILLY.

That being said... I'm decent at math, and I'm fairly certain that if I had taken a class that actually taught trig I'd get it without too much problem. Keyword there is "without too much"*. I would have a single, huge, impassible problem.

MATH IS BORING!

How some people can stare at a huge strong of numbers and work it out without going mad from boredom is something I've never been able to understand. It's like reading shakespeare backwards... long, complicated, and no real benefit in the end.


*I am fully aware that this was three words.

[Fiery Diamond]

If you think its painful now, Wait until you mix trig with calculus and start differentiating and integrating with these little guys

AAAAHHH!

Yes, I completely concur with this statement. Ugh.

[some_other_dave]

You need to study trig because otherwise you'll never understand why e^(i*pi)+1=0.

Conversely, if you do study trig, you'll never understand why e^(i*pi)+1=0. ;)


Trig, back in HS, was OK. I have used part of it a lot since graduating college, but only with right triangles. (Working in a Cartesian space, comparing anything to the axes--which is a very natural thing to do--reduces to playing with right triangles.) SOH-CAH-TOA has been my friend for many many many years. So has the "small angle assumption", that sin(x) ~= (x) for small x.

-soD

[lord of kobolds]

I'm in precalc in freshmen year of highschool, and even I hate trig.
solve sin 90 without using the unit circle!!!

evilevilevilevilevil

[DanielX]

I'm in precalc in freshmen year of highschool, and even I hate trig.
solve sin 90 without using the unit circle!!!

evilevilevilevilevil

Sin 90... do you mean 90 degrees or 90 radians? They're both easy....

Sin (90 degrees) = 1 (90 degrees = 1 radian)
Sin (90 radians) = 0

Its things like Sin(65.3) or something that's :smallfurious: hard....

[unstattedCommoner]

Conversely, if you do study trig, you'll never understand why e^(i*pi)+1=0. ;)


By definition.

Expand cos(x) + i*sin(x) in series. Compare with the series expansion of exp(i*x). Set x = pi.

This only works because, being solutions of d^2f/dx^2 = +/-f, exp, sin and cos are complex analytic functions and because the limit of a complex series is defined as "add the real and imaginary parts separately".

@DanielX: 90 degrees is not 1 radian. 90 degrees is pi/2 radians.

[MeklorIlavator]

sin(90) in radians doesn't equal 0, it equals .893997.... In radians, sine of 0, pie, 2pie, and all values x, where x=k(pie) are equal to zero.

And what really hurts is finding the area between 2 polar functions, especially when they intersect at more then one place. Or finding integrals/derivatives of trig complex functions. Really, no one expects you to do sin(65.5) in your head unless your using taylor series, and in that case there are worse things that they can do to you.

[Player_Zero]

Good ol' power series...

I do keep on going on about it, but in STEP, one of the questions I just had a look at was finding an approximation for root(2) using the binomial expansion dealie... It was quite neat.

And yeah, you don't get a calculator for these exams, you've just gotta' rely on guts and determination.