BobbyJoeCool

Now switch pi over 4 and pi over three so you get -pi over 12... you'll get the same answer!

EDIT: Delete

[math]\cos{\tfrac{-\pi}{12}}=\frac{\sqrt{2}(\sqrt{3}+1)}{4}[/math] [math]\cos{\tfrac{\pi}{12}}=\frac{\sqrt{2}(\sqrt{3}+1)}{4}[/math] (Checked using TI-89 Graphing Calculator in Exact mode (AND radian mode)). Think of the graph of cos... at x=0, y=1... it is symetrical as to the y-axis (as in, if you move the same distance from the y-axis in either direction, you have the same y value...) Therefore, [imath]\cos{x}=\cos{-x}[/imath]

association is one thing, also drafting (being able to see objects from many different angles in your mind.). I really don't know for sure, but these sound right, you might check into it...

ahh... a "to-do" list... I love those... I think I have about 4 of them, some of which I'm 2 weeks behind on... Oh well, such is my life right now.

Most IQ tests in America are Stanford-Binet IQ tests... Otherwise, there's WEIS, and I can't think of any others... If you are under 16.. WISC, and under 6? it's WCCIP (I think...)... Ring a bell?

Because, its a continous function, so there's a patern. EDIT: (c is the distance between x and a) look at that graph... the point (x,f(x)) is one point on the secant line right? and the other is (x+c,f(x+c)) right? and the derivative is the slope of the tangent line right? so, you move the point (x+c,f(x+c)) closer and closer to (x,f(x)) (in other words you make c smaller and smaller until it's zero)... the whole time, the slope of the secant line will be [imath]\frac{f(x+c)-f(x)}{c}[/imath]... being [imath]\frac{\Delta y}{\Delta x}[/imath], right? (please note the c IS the change in x). So, what happens to the graph as you make c closer to 0? The secant line moves closer to being the tangent line, right? and when c is 0? That's right! It's the Tangent line!!! The problem however, is that now that you have a tangent line, the equation for slope has become [imath]\frac{f(x)-f(x)}{0}[/imath], which is 0/0. But, we get around this, because as long as c does not equal 0, the equation for the slope is defined. so we need to find the limit on the function as c goes to zero.... So the [imath]\lim_{c \to 0}\frac{f(x+c)-f(x)}{c}=f'(x)[/imath] where f'(x) is equal to the derivitive, which is the slope of the tangent line. In order to get the answer you need to get the c out of the denominator (which can be difficult), but this is the definition of a derivative, and any proof involving derivatives will involve this somehow... Any better?

I was noticing in the main screen (not the forum index), the link that says Contact Moderator hasn't been updated recently (ie: to include Pangloss and Mokele, and is Dudde back?) I think you should either change the link to Forum Leaders (which is correctly updated), update the post which has mods/admins or both...

Try to name more than two psychologists before Freud. WITHOUT looking them up... Can you do it? How about after Freud? He brought psychology into the view of the pubic eye, thus people started to care about it, and thus people started actually researching it more than it had been in the past. Most of his theories were wrong, but that's ok. It's not science unless somethings are proven wrong!

That sounds very Freudian... even though there's nothing about Sex in it... It's a point of view, and it makes sence. I like the one I tried to explain, (having been only exposed to a couple by my various psych teachers)

Limit... the limit on a function f(x) as x approaches a certain value... take x^2 for example... as x goes to zero, the values of the function get closer and closer to 0 from both sides, so [imath]\lim_{x \to 0}x^2=0[/imath]. Now, you might be saying, well it's just the value of the function at that given point, right? well, almost. But that's more complex. A derivative is quite simply the equation for the slope of the tangent line of a function. (denoted f'(x)). So, if f© and f'© both have values, then f'© is the value of the slope of the tangent line to the equation f(x) at the point x=c. Does that help? (If you don't get it, you'll just have to wait till you take Calculus...)

Is the bar gone completely? If it is, you can move the mouse close to the bottom and click and drag it up (much like you do to make a cell larger or smaller in Microsoft Excel) (you can make the bar disapear by doing this the other way, and make it take up the whole screen by going up)... Otherwise, can't help ya Sundance...

For the record... Id, Ego, and Superego are all Freudian... and it's one school of thought on the subject (and most of Freud's thoughts are concidered not true per se anymore).... You subconscious mind is the part of the mind that you are not aware of. Like when you get into a routine, and you say "I could do that in my sleep." that's because you're conscious mind is thinking about/trying to solve some problem while your subconscious mind is going through the same routine that you go through every day. Driving is a good example... Your conscious mind can be talking to the person next to you, thinking about what you're going to tell you boss because you're 2 hours late... etc, and when you get where you're trying to go, you suddenly think, "I wasn't thinking at all about actually driving here..." That's because while you had more pertinant things on your mind, you subconscious took over the "easy" driving (because, for the most part, it can be done robotically). Now this is ok, because, say a kid runs in front of your car, you subconscious signals your conscious to take over because something different has happened and you need actual thought to decide what to do (which all happens in about .1 seconds). I can attest to this at work... as a fast food worker, all the tasks are so menial that I can do them without thinking (subconsciously)... Now, it's faster if I'm completely focused on what I'm doing, but I can actually solve many problems, think many things over etc. while doing 8 hours of work, because that's how routine my job is (same thing, day in, day out). Some say that it becomes "second nature." Which is another way of saying the subconscous takes over. Also, iirc, your brain processes close to 500 inputs at any given time, but you only consciously process about 10... You still notice things you process in your subconscious, but it's those situations where you "can't put your finger on it..." A situation seems farmilliar because it's a lot like one you've been in before, but you only consciously remember the other occurance by what you consciously "saw" and not as a whole, and since you're looking at things differently, it seems different, and yet it seems farmilliar. De ja vous is a good illustration of this. (I don't know if you understand what I'm saying, but I know it, and maybe if you ask more specific questions, I can better answer) Now, that's what subconscoius is... Now to the rest of your questions... Thoughts are primarily the domain of the conscious mind. Because, if you view thought as speaking to yourself without talking, you are always aware of what's being said. The subconscious can influence what's on your conscious mind. Such as, when you're looking at a situation, you don't really notice that the leg of a chair is about to break (because it does so slowely), but you have a gut feeling that you should pick your child up out of the chair, and not long after, it breaks and you say, "Well, that was lucky!" This could be seen as your subconscious telling your conscious that something was happening, and you should do something... When you argue with yourself, it's entirely conscious. It's you trying to figure out the solution to a problem by trying to view it from different viewpoints (which, I've found, is the best way!). When you make a decision when you want the other, it can be for many reasons... A) you can realize that what you want isn't what's best. B) you might be doing it to prove to yourself just how screwed you are... (depression can cause this) C) you might be trying something different (not doing what you want...) etc... You're subconscious mind can't "take over" your conscious mind. If you're reffering to a situation such as in the movie Psycho (Hitchcock) (if you haven't seen the movie, and don't want a spoiler, skip the rest of this paragraph), where he has both the personalitles of him and his mother... this is a mental disorder called MPD (Multiple personality disorder). Both personalites exist in the conscious mind. And at times, the "mother" became stronger than his, and took over. But everything that happened was in the conscious mind. That's one way of viewing subconscious... it really is just what you don't realize your brain is doing (regulating breathing, and the rest of my examples are good examples). It can be working on problems just like your conscious mind, but it's not as good at it (because (mostly) logic exists in the conscious mind and not in the unconscious...). You subconscious isn't very good at all at "thinking for itself" (hence in the car example, when the kid appears, it signals the conscious to take over because it doesn't know what to do). And, no it doesn't have a personality of it's own... it has no real personality at all... it's a place where routine things get done. (kinda like a subroutine of a program.) You can "program" your subconscious to do things much like a computer, but it can't handle creating logic on it's own. You can "train" it, but if you have to deviate from what it's trained to do it won't know what to do and the conscious mind has to take over. Which is why, if we go back to the work example, a job were all the tasks are menial and routine, it does take some conscious thought to orginize what to do... Like, my subconscious can count the drawers, count the deposit, make sandwiches, take orders (MOST orders, I should say...), bag and hand stuff out, etc... but orginizing it so that it all gets done in a timly/orderly fashion takes some conscious thought (knowing which subconscious "subroutine" to call, and at what time.) See the previous section... it doesn't really have it's own thoughts, so you can't really read them. And when you become aware of what it's doing, it becomes conscious thought, and no longer subconscious. When you make a desicion (if it's one you have to make regularly, like what should I wear today?), it can be handled subconsciously (if you're male that is... jk.) because it's more of a what matches with what, or even, what's clean, rather than what's the best way to get from point a to point b. You can't ask your subconscious for advice, per se, but it can make minor desicions without need for conscious thought... Home I helped you Herme...

You're way isn't shorter... just you don't show all the steps like I did... You got (2sin•cos)cos because [math]\sin(2a)=\sin(a+a)=\sin(a)\cos(a)+\sin(a)\cos(a)=2\sin(a)\cos(a)[/math] and [math]\cos(2a)=\cos(a+a)=\sin(a)\sin(a)-\cos(a)\cos(a)=\sin^2(a)-\cos^2(a)[/math] I mearly showed those steps, so it looks longer, and I still like my final form better!

Given [math]\sin(\alpha+\beta)=\sin(\alpha) \cdot \cos(\beta)+\sin(\beta) \cdot \cos(\alpha)[/math] and [math]\cos(\alpha+\beta)=\cos(\alpha) \cdot \cos(\beta) - \sin(\alpha) \cdot \sin(\beta)[/math] and [math]\sin^2(\alpha)+\cos^2(\alpha)=1[/math] you can figure it out... [math]\sin(3\alpha)=\sin(2\alpha+\alpha)[/math] [math]\sin(2\alpha) \cdot \cos(\alpha)+\sin(\alpha) \cdot \cos(2\alpha)[/math] [math]\sin(\alpha+\alpha) \cdot \cos(\alpha)+\sin(\alpha) \cdot \cos(\alpha+\alpha)[/math] [math][\sin(\alpha) \cdot \cos(\alpha) + \sin(\alpha) \cdot \cos(\alpha)] \cdot \cos(\alpha)+\sin(\alpha) \cdot [\cos(\alpha) \cdot \cos(\alpha) - \sin(\alpha) \cdot sin(\alpha)][/math] [math]2[\sin(\alpha) \cdot \cos(\alpha)] \cdot \cos(\alpha)+\sin(\alpha) \cdot [\cos^2(\alpha)- \sin^2(\alpha)][/math] and if... [math]\sin^2(\alpha)+\cos^2(\alpha)=1[/math] Then [math]\cos^2(\alpha)=1-\sin^2(\alpha)[/math] [math]2[\sin(\alpha) \cdot \cos^2(\alpha)]+\sin(\alpha) \cdot [1-\sin^2(\alpha)- \sin^2(\alpha)][/math] [math]2[\sin(\alpha) \cdot \cos^2(\alpha)]+\sin(\alpha) \cdot [1-2\sin^2(\alpha)][/math] [math]2\sin(\alpha)[\cos^2(\alpha)+1-2\sin^2(\alpha)][/math] [math]2\sin(\alpha)[1-\sin^2(\alpha)+1-2\sin^2(\alpha)][/math] [math]2\sin(\alpha)[2-3\sin^2(\alpha)][/math] [math]4\sin(\alpha)-6\sin^3(\alpha)[/math] however... from this step... [math]2[\sin(\alpha) \cdot \cos(\alpha)] \cdot \cos(\alpha)+\sin(\alpha) \cdot [\cos^2(\alpha)- \sin^2(\alpha)][/math] [math]2\sin(\alpha)\cos^2(\alpha)+ \cos^2(\alpha)\sin(\alpha) - \sin^3(\alpha)[/math] can be reached (which is slightly different from your answer), but my form is simpler! (last step edited by realizing my mistake...)

I agree... IMM is awsome with the Relig/Phil. She knows the most about them of anyone I've met. And yea, she has the heart for it! and... aww, she's modest too...

love it!

It calculates the age as you go along (top right corner), but isn't on the final screen...

http://www.nmfn.com/tnetwork/longevity_game_popup.html This game calculates how long you'll live... It's kinda fun. I'm out at 84...

little nitpick... you say: but if f(x)=cubed root x' date=' and you say [math']f'(x) = \lim_{h\to0} \frac{f[(x + h)^{1/3}] - f(x^{1/3})}{h}[/math] What you're really saying is... [math]f'(x) = \lim_{h\to0} \frac{[(x + h)^{1/3}]^{1/3} - (x^{1/3})^{1/3}}{h}[/math] because you already put the (x+h) into the funciton when you put the (1/3) as the exponent, but now you're saying (by taking f((x+h)^(1/3))) that you want to put it into the function a second time...

first priciple... (The definition of a derivative) [math]f'(x)=\lim_{\Delta x \to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}[/math] so... [math]f(x)=x^{1/3}[/math] [math]f'(x)=\lim_{\Delta x \to 0}\frac{(x+\Delta x)^{1/3}-x^{1/3}}{\Delta x}[/math] EDIT:Some people replace "Delta x" with h or y. Matt replaced it with e...

And, there is a thread somewhere that does show it step by step...