Math Help

Comprox

OK, I feel pretty stupid asking this (and none of my friends are around/being helpful), but after taking 1.5 years off school, I can't see what the heck to do. I need to prove these 2 identities are the same:

(sin x + cos x)^2 = 1 + sin 2x

So far the only step I know is making the right side 1 + 2 sin x * cos x

I am really not sure how to break down the left side. It's not the same as (sin^2 x + cos^2 x) or (sin x^2 + cos x^2), so I am not sure what to do.

Rellix

(sin x + cos x)^2 = 1 + sin 2x

sinx*sinx + 2(sinxcosx ) + cos*cos =RHS (Right Hand Side)
(sinx)^2+s(sinxcosx)+cosx^2


Eh from then on i forget.

WishCow

Well, english is not my primary language, but I'll try to help.
According to this:
(a+b)^2 = a^2 + 2ab + b^2 (The first tag is, the first tag powered by 2, the second tag is the product of the tags *2 (so here it's (a*b)*2) and the third tag is, the second tag powered by 2.

This should be same, just not with a+b.

Hope this helps, someone correct my spelling please, I'm not really sure about "power" and "product".

Comprox

And then Sin x^2 + cos x^2 = 1
so it becomes 1 + 2sinxcosx which = RHS

Awesome, thanks <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin-fix.gif' border='0' style='vertical-align:middle' alt='biggrin-fix.gif' /><!--endemo-->

Rapier7

Comprox:

Goddamnit, I took this all last year, but I forgot all of it.

sin x + cos x to the ² power equals something, I forget.

It's actually an extremely easy problem, but you have to memorize some formulas to make it that easy.

I can't remember, it, though. But I hope that sends you in the right direction.

taboofires

<a href='http://www.math2.org/math/trig/identities.htm' target='_blank'>trig identities</a>

That aughta help alot.

Soylent_green

instead of remembering lots of trigonometric identities just remember the euler identity (e^ikx = cos kx + i sin kx) and you can prove most of them easily.

e.g:

(note: sin x is odd and cos x is even, sin -x = -sin x, cos -x = cos x)

cos x = (e^ix + e^-ix)/2
sin x = (e^ix - e^-ix)/2i

2cos x * sin x = (e^ix + e^-ix)*(e^ix - e^-ix)/2i = (e^2ix -e^0 + e^0 - e^-2ix)/2i = sin 2x

edit: If you don't quite get what something means try taking it in as small steps as possible. Don't rely on memorizing stuff without understanding, it will only hurt you in the end. Expanding a square in a bunch of easy steps: (a + b)^2 = (a + b) * (a + b) = a(a + b) + b(a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2.

First the definition of exponentiation is used( a^n = a * a * a.... *a, n times), then the fact that multiplication is distributive is used twice( a(b + c) = ab + ac), then the fact that it's commutative is used ba = ab. All these steps are really obvious.

sin^2 x is just a slightly more confusing way of writing (sin x)^2, don't confuse it with sin x^2 = sin(x^2).

That_Annoying_Kid

=\ Math is one of the things that I suck at, college is going to be hell with that handicap, but I shall overcome!

OttoDestruct

I'm doing derivitives right now. It sucks.

Firestorm2

Multiply the left side out. The square

you will see sin(x) squared + cos(x) squared + 2 sinx cosx = 1 + sin2x. You should well know that sin(x) squared + cos(x) squared = 1. The big 1 on the right side should tip you off to use that identity, if you have an inkling of it still in memory.

So you have 1 on both sides. Drop both and you end with 2 sinx cosx = sin 2x which evidently is an identity, <b>this</b> identity in fact:

2 sinx cosx = sin 2x = sin (x+x)

you can find the sin (x+x), cos (x+x), etc formulae/identities in any math book that deals with these. You can even find proofs probably XD

Nil_IQ

I've forgotten all the maths I ever learned, and i'm going to uni in 9 days. Looked at my old textbook for nostalgia and its complete gibberish to me now.

BUT I DON'T NEED IT IN THE REAL WORLD! HUZZAH!

Firestorm2

don't need English class in the real world either
I'm better than all those newbs

UltimaGecko

The NS Forums aren't around to help you do your homework...

<span style='color:red'>*LOCKED*</span>







<!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin-fix.gif' border='0' style='vertical-align:middle' alt='biggrin-fix.gif' /><!--endemo-->



If you manage to test out of math...you convienently don't need to take any math classes. Conveniently enough I've never taken anything above algebra 2 with trig functions.

If you can do algebra you should be able to work through GDR college credit classes, so I think you'll be fine, Nil.


And English classes are so you learn how to write better than "I r going 2 the clock 2nite." Once you get to higher grades they're basically literature classes and trying to find annoying literary techniques in writing <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> .

Real world geometry applications:
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->"Now, you want to get to Bakersfield? Okay, first you go down this road, you'll see one road going perpendicular and one going parallel, there will be one road bisecting the parallel road at a 25 degree angle, solve for x."<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->-poorly paraphrased from Family Guy

...or not. Pffft, the only time you need high level maths are if you're in a high level math career, like programming or engineering.

Bijiy

This thread hurts my face. :'(