Foo - Trig identities

This trig class so far has been pretty easy, due to the exposure from Physics. But this one assignment is pretty annoying, I am not getting anywhere. THis makes me think of a sort of a puzzle where you have to just do it a few times to get your mind 'in gear'. Okay well then my clutch is shot or something. We never got to see an example problem done, the teacher was in sort of a rush and gave us this. She said basically "if one method doesn't work, try something else". Well, I am going to be here all night at this rate. Can somebody give me a jump start? We are supposed to simplify problems like this:
[(1-tan^2)/(1+tan^2)]+2Sin^2

Farthest I've gotten is to realize that 1+tan^2 = sec^2 :D

Maybe this may help:

http://mathforum.org/dr.math/faq/formulas/faq.trig.html

i used to hate trig identities, but once you understand them, and use them in some calculus problems, its actually pretty fun solving those problems.

Farthest I've gotten is to realize that 1+tan^2 = sec^2 :D
To me, this looks like shorthand for the assertion that getting a tan doubles your chances of having sex (which may or may not be true, but I have a hunch it is not what the author intended to communicate here).

This astounding level of math comprehension is one of the primary reasons I ended up in law school. Let this be a warning to you, kids.

Doesn't that just equal 1?

yes it does equal 1,

pc2, try subs for tan^2 -> (tan^2 = sin^2/cos^2)

then fiddle with the 1('s)

its actually pretty fun solving those problems.

agreed, like solving a puzzle, very useful in calc too!

We never got to see an example problem done, the teacher was in sort of a rush and gave us this.

Sorry to crash your thread but... you've just tickled a pet peeve of mine. I'm not saying you're whiny, but I can't stand it when students whine about "we've never seen an example!!!!". Usually, that's the idea! Every good test contains new material, IMO. How else is one to learn as opposed to merely memorize?

Anyhow let me join the chorus to confirm that the expression does simplify to unity (i.e. is equal one). My hint? Use the identity you cite on the denominator and go from there. It should fall out in front of you.

Glad to hear that someone out there approves of the way I intend to write my tests in the future.

Yikes, I've even forgotten that basic stuff. And I have a math degree :eek:

This is the one thing in math I never managed to get through properly. I hated it, and still hate it, with a passion.

It's these types of problems, the puzzle problems. Those types of things come up once in a a while, and I never liked them. In science, I enjoy learning and discovering. Raw math, in SOME instances (like this)...I need a jump start :D. I will look into 1, I stopped last night and decided to use another side of my brain instead.

One quick question, she wrote down that
tan = sin/cos

I knew this, and have actually used this in Physics on projectile motion problems (on this forum even). She never mentioned that Cos*tan = Sin though. Or that Sin/tan = Cos. Is this actually the case, or does rearranging not work in this instance?

i used to hate trig identities, but once you understand them, and use them in some calculus problems, its actually pretty fun solving those problems.
I'll agree with that. I've already found some of the basic identities useful, and I am not taking calculus or calc based physics. And, these types of things are *slightly* fun, when you get the hang of it :p

One quick question, she wrote down that
tan = sin/cos

I knew this, and have actually used this in Physics on projectile motion problems (on this forum even). She never mentioned that Cos*tan = Sin though. Or that Sin/tan = Cos. Is this actually the case, or does rearranging not work in this instance?

Think about basic algebra for a moment, heck, not even that far ahead, basic fractions and it should be clear why all three are equivalent. The only situation this sort of thing doesn't work is if one divides by zero which usually is an illegal operation or at least is considered to give results that don't make any sense. Can sin = 0? Can cos = 0? Of course! So you have to keep in mind then that sin(theta)/cos(theta) = tan(theta) but is not defined for theta which give cos(theta) = 0, etc. Another way to understand this is by constructing the trigonometric functions from a right triangle, example (http://id.mind.net/~zona/mmts/trigonometryRealms/introduction/rightTriangle/trigRightTriangle.html) (since you like examples LOL).

Jschen I was thinking when I wrote my first reply of saying, "and no doubt jschen will back me up on this". Guess I was right. :D

Subs, get everything like terms (if you want to do it the long way):
tan2(x) = {(1 - cos[2x])/(1 + cos[2x])**
sin2(x) = {(1 - cos[2x])/2**

Then simplify expression ---- = 1

Hint to make the algebra easier take the like terms (i.e. 1-cos(2x) and 1+cos(2x) into holders A and B). Makes the algebra easier for me.

If you want to see what I am talking about just PM me.

http://www.geek.com/pdageek/features/chic/pocketpr.gif

Trig identitites are the most annoying things in the world. Don't ever waste time learning them. Find a friend who's super good at math, and when identities are needed in real life (they are sometimes, but almost never, unless you're a mathematician, who are just crazy), ask the aforementioned friend.

If you decide to pick just one, remember sin^2 + cos^2 = 1. I've seen that one a few times in engineering. The others almost never.

http://www.geek.com/pdageek/features/chic/pocketpr.gif
Urm. I have one of those. :o And several sliderules, too. And I know how to use them! :eek:

Sliderules are not geek. These days, they are retro.

One quick question, she wrote down that
tan = sin/cos

I knew this, and have actually used this in Physics on projectile motion problems (on this forum even). She never mentioned that Cos*tan = Sin though. Or that Sin/tan = Cos. Is this actually the case, or does rearranging not work in this instance?

I haven't seen anyone else mention this yet...hope I didn't miss anything.

These are easy.

sin = opposite / hypotenuse (from now on abbreviated opp/hyp)
cos = adj / hyp
tan = opp/adj

cos * tan = (adj / hyp) * (opp / adj)
simplify: (opp / hyp) = sin

Ex. 2: sin^2 + cos^2 = 1
(opp / hyp) * (opp / hyp) + (adj / hyp) * (adj / hyp) =
(opp^2 + adj^2) / (hyp^2)
Since we're dealing with a right triangle, remember opp^2 + adj^2 = hyp^2 (pythagorean theorem: x^2 + y^2 = z^2)
so,we have (hyp^2) / (hyp^2) = 1

Good luck with it.

Sliderules are not geek. These days, they are retro.
They've never been geek in my book. Perhaps retro today, they were simply de rigeur in the day. ;)

I haven't seen anyone else mention this yet...hope I didn't miss anything.

These are easy.

sin = opposite / hypotenuse (from now on abbreviated opp/hyp)
cos = adj / hyp
tan = opp/adj

I've always used "Ollie Had A Hairy Old Arm" to remember.

They've never been geek in my book. Perhaps retro today, they were simply de rigeur in the day. ;)
Yeah, but it was the monogrammed holster that made it geek chic. Compared to that, even the modern Blackberry-stuffed Bat Utility Belt is tame.

Got the holster. Leather. :D

I've always used "Ollie Had A Hairy Old Arm" to remember.

I learned it:

sin (theta) = y/r
cos (theta) = x/r
tan (theta) = y/x

Never bothered with opposite or adjacent sides... just which was X, Y, and R... To keep it memorized, I just remembered how sin(theta) runs on a graph... for numbers close to zero, sin(theta) = theta.

I have only ever failed two classes in my entire scholastic career: The most recent was Trigonometry when I was a junior in highschool.

(The other one was Penmanship when I was in 1st grade.)

for numbers close to zero, sin(theta) = theta.
My first-year calc prof was awesome, and we had a similar sense of humor [1]. So he was putting stuff on the board one day, and he slipped that little bit through without mentioning it. So, me being me, I raised my hand and asked "did you drop the sin around the theta?"
Him: "No...for small values of theta, sin(theta) = theta."
Me: *pause* "Bullsh*t..."
The class cracks up, and he takes a moment or two to prove it. It was great.

[1] This started with him jabbing me on the very first day of class. He had an eyepatch. He was doing something in 3d, and he described an arc on the board and drew perfect projections. I was having trouble seeing how one curve projected into one of the planes and asked how he could see it projected there.

Him: "Easy...just close one eye..."
From there it started. I wound up grading for him the next year. Awesome guy. Wonder if he's still there...

I've always used "Ollie Had A Hairy Old Arm" to remember.

We were taught about an indian named Sohcahtoa. Then you know, that became politically incorrect so we were told not to use that anymore :rolleyes:

Maybe I should start posting my HW up here for some of you guys to do.