in trinomial 2sin^2x+sinx-1=0, if i am to factor it with (sinx=u), shouldn't 2sin^2x become something else rather than u^2? if U is sinx, shouldn't U^2 be sin^2x^2?

Guest Jun 8, 2014

#13**+14 **

Call the constable of the guard!

A band of pirates hath hijack the special, private label elixir intended for Rom, the Master of Physics and Numbers.Surely he be disappointed.

The pirates have not sought a ransom, Perhaps, they prefereth the contents to the ransom. No matter. I shall order the scribes to create another, superior label for such a master. He is truly worthy!

------------

Top of the day to you, Sir Cphill.

Your coat of arms doeth represent with a certainty and assurance the great world where we liveth hath room for satire and irony.

In my dominion, such icons be rare or be not recognized for what they meaneth . ---------

Morgan^{-1} Tud

MorganTud Jun 9, 2014

#1**+5 **

No,

$$2sin^2x+sinx-1=0$$

Let u=sinx

$$2u^2+u-1=0\\\\$$

to factor this I will look for 2 numbers that multiply to 2*-1=-2 and add to 1 (the invisible coefficient of x)

+2 and -1 work. so I am goiing to split up 1u into 2u-1u

$$2u^2+2u-1u-1=0\\\\

2u^2+2u-1u-1=0\\\\

2u(u+1)-1(u+1)=0\\\\

(2u-1)(u+1)=0\\\\

u=0.5\qquad or\qquad u=-1$$

so

sinx = 1/2 or sinx=-1

etc

If you do not understand this tell me what the problem is and I will explain some more.

Melody Jun 8, 2014

#2**+5 **

The convention in mathematics (as opposed to computer software) is that sin^{n}x (and cos^{n}x etc.) is usually the same as (sinx)^{n}.

There is one exception, and that's when n = -1. So sin^{-1}x is *not* the same as (sinx)^{-1}.

sin^{-1}x is the inverse function arcsine (or asin). It is the angle whose sine is x.

I don't know what genius decided this should be the case, but it's led to confusion for millions down the years!!

Alan Jun 8, 2014

#3**+5 **

Yes Alan, I'd like to know who decided this as well. I'd ring his neck. It's bound to be a male!

Where did this sin^{-1}(x) notation ever come from?

asin(x) is infinitely better notation!

Melody Jun 8, 2014

#4**+11 **

asin(x) is infinitely better notation!

----

I guess it is "a sin" that it's not.

If it were, then "a sin^{-1}" would be a good deed, instead of a transgression.

Would that not be so, M' Lady?

Moragn Tud

Guest Jun 8, 2014

#5**+5 **

Good day to you Chiurgeon Tud, it is indeed a sine. A sign that men of mathematics can indeed lack logic. Perhaps this notation was cemented after an evening of celebration? Perhaps a little liquid logic had been poured forth. What think you my good Doctor? I see that thou have a problem with the spelling of thine name. Perhaps thou too have had a toddy or two?

Lady Guinevere.

Melody Jun 8, 2014

#6**0 **

"Moragn" Tud is just another way of writing Morgan^{-1} Tud. He often sines his name that way...........

CPhill Jun 8, 2014

#7**0 **

I never noticed before - thanks Chris.

I did a search and cannot find it spelt like this anywhere else!

So I say to you Sir CPhill - you are making that up!

Lady Guinevere.

Melody Jun 8, 2014

#8**+11 **

Aye, m’Lady, undeniably, I have prescribeth for mine self a finest of tonics.

This inst., I visit with a Capitan of the Scottish navies. Morgan be his name and that of his family.

The Capitan offereth the finest of whiskies that he calleth “plaid,” and it be so hot, that one need not set it alight to keepth warm. Indeed, I now undersandeth why the dressage here be so airy.

When I returnest to thine kingdom, a barrel of this Scottish tonic I shall bring as a gift for m’Lady and her Royal House.

For Sir CPhill, I will prescribeth, that he may desire to break again from his quest for the Roman Zero, and add to my new mark that becometh part of my coat of arms.

With the prescription, I must warn: breathe not upon a candle or lamp, lest thou find the breath of a dragon blazing before thy face.

By your leave.

In your service,

Morgan^{-1} Tud

Guest Jun 8, 2014

#9**+5 **## Queen Guinevere.

I doth understand why thou hath such problems spelling out thy name.

Tis difficult with such liquids running through thy veins.

I have a comprehension problem What doth thou mean by this?

"and add to my new mark that becometh part of my coat of arms."

How can Sir CPhill help with this? Explain forthwith!

By order of the land.

For those of you who may have problems following the thread, Chiurgeon Tud is aluding to his favour of the liquids thus portrayed.

Melody Jun 8, 2014

#10**+14 **

Aye, Lady Guinevere,

Sir CPhill hath helped forthwith.

As an alchemist be with the elements, so be Sir CPhill with numbers. IF there be any in thy land who may find the Roman Zero, it be Sir CPhill. He doeth magic on numbers as Morgan le Faye doeth her sorcery on the land and its vapors. He, by his math magic, gave great power to the Morgan name, though it be not a number. The spell he useth be this: Morgan^{-1}. It be set in the Morgan coat of arms as thus: M^{-1}

This inversion causeth (Morgan^{-1}) =NagRom. I find in this, great honor and humor. Indeed, Capitan Morgan gavest me a very special elixir for the Math-Magicians of thy land. It be labeled and named for the great Master of Physics and Numbers. A mulish, nag that on occasion speaketh –a gift from Morgan La Feye -- carrieth the elixir. Therefore, all who be Morgan will find great honor, if he wish to use it as his coat of arms.

By the magic of the crystal sphere, I send thee an image, that the Master of Physics and Numbers may have the privilege of her Majesty presenting it to him by her person.

In Your Majesty’s service,

Morgan Tud

Math Proof

MorganTud Jun 8, 2014

#11**+8 **

Thankee mightily, Morgan ...( or, if I can use thy formal appellation..Morgan^{-1} )

Thou elixir has given me great insight into the possessor of the object of mine quest...I should have suspected all along that it was the Great and Powerful Rom who holds the "Rom"an Numeral that I search for......I must must proceed carefully, however....It is known in the land that his "thirst" for power(s) is unrestrained by any bounds or limits.......mathematically speaking, of course

No thanks to Sisyphus, either....that lout and cad !! I should have known all along that he was worthless....a real sypher, if you will......

I had made gift of flowers and chocolates for Lady Guinivere who celebrates her birthday this day. Apparently, they were unappreciated!! I think I will throw in Sisyphus as "lagniappe." ....(even though current records indicate that M'Lady was born on or about April First.....a noted US holiday..... fitting for one so regal..........)

Your Humble Servant,

Sir CPhill

CPhill Jun 8, 2014

#12**+5 **

What is this nonsense that you speak Sir CPhill?

I entreat you to repent for it is a great injustice that you do me Sir.

Perhaps without your head you have no eyes to read for I know not how I could be more gracious.

http://web2.0calc.com/questions/most-questions-are-answered-and-the-end-of-day-wrap-is-written-sunday-8-6-14#r7

Melody Jun 9, 2014

#13**+14 **

Best Answer

Call the constable of the guard!

A band of pirates hath hijack the special, private label elixir intended for Rom, the Master of Physics and Numbers.Surely he be disappointed.

The pirates have not sought a ransom, Perhaps, they prefereth the contents to the ransom. No matter. I shall order the scribes to create another, superior label for such a master. He is truly worthy!

------------

Top of the day to you, Sir Cphill.

Your coat of arms doeth represent with a certainty and assurance the great world where we liveth hath room for satire and irony.

In my dominion, such icons be rare or be not recognized for what they meaneth . ---------

Morgan^{-1} Tud

MorganTud Jun 9, 2014