
		Fabrice Faure
 
		FFaure2@aol.com

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	Linearization program:  
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Linearize sin^N1(n1)*cos^N2(n2)

Enter the 4 coefficients.
Ex: if you want to linearize (sin ^2(3x))*(cos 4x) enter N1=2;n1=3;N2=1;n2=4
 or if you want to only linearize sin^2(3x) ( =sin^2(3x)*1 =(sin^2(3x))*(cos^0(x)) enter N1=2;n1=3;N2=0;n2=1
Then the program display the results in 4 parts , exactly as if you have calculated it yourself (now you couldn't make errors and lost time in boring calculations ;) )
Say we want to linearize sin^2(3x)*cos^3(x)
Enter N1=2;n1=3;N2=3;n2=1
1 St:
{f(x)=1/
{		(-32,0)
{*
so f(x)=1/(-32) because (-32,0)=-32+0i for the Ti-85
Then you could see two items on the menu bar:SIMPL and DTAIL
Let's start with the DTAIL item: it display the expression in symbolic form (exactly in the same way as you would write on you paper) but it take a little time to the TI for calculate the expression
On the screen you would see
{f(x)=1/
{		(-32,0)
{*
{ +1e^(+6ix)-2+1e^(-6ix)
If you can't see all the expression you could make it scroll with the arrows keys.You must simplify it a little and write "e^(6ix)-2+e^(-6ix)" (it's because it would be slower if i make other test to determine theses conditions.

Then press the enter key and press the DTAIL menu item: you would see:
{f(x)=1/
{		(-32,0)
{*
{ +1e^(+6ix)-2+1e^(-6ix)
{*
{ +1e^(+3ix)+3e^(+1ix)+3e^(-1ix)+1e^(-3ix)
So f(x)=(1/-32)*(e^(6ix)-2+e^(-6ix)*(e^(3ix)+3e^(ix)+3e^(-ix)+e^(-3ix)

2nd Part:
Press enter then DTAIL again:
{f(x)=1/
{		(-32,0)
{*
{ +1e^(+9ix)-2e^(+3ix.....
Now the polynom is developped
Simplify it in the same way as before
3nd Part:

Press enter then DTAIL again:
{f(x)=1/
{		(-32,0)
{*
{ +1e^(+9ix)-1e^(-9ix.....
Now the terms of the polynom are grouped 2 by 2

Last Part:
Press enter:
{f(x)=1/
{		(-32,0)
{*
{ +2cos (+9x)
Press enter the number of times for the program to stop(if there is an error at the end ,the result is correct, don't ask me why there is an error i haven't find why but you could be sure that the result would be true) 
{*
{ +2cos (+9x)
{ +6cos (+7x)
{ +6cos (+5x)  
{ -2cos (+3x)
{ -12cos (+1x)
So f(x)=-1/16*(cos 9x+3(cos 7x)+3(cos 5x)-2(cos 3x)-12(cos x))
It's finished !

If instead of the DTAIL item you press the SIMPL item the expression is displayed in a different way but it is a lot fastest
Instead of displaying +1e^(-3ix)-2e^(5ix) you would see:
{(1,-3) (-2,5)}
The format is f(x)={(x1,y1) (x2,y2) ...}
where f(x)=x1*e^(y1*ix)+x2*e^(y2*ix)

!!!!!! Don't forget if the TI says there is an error at the end of the program ,the result that is displayed is true.


English is not my native language so send me spell-correction if you wish.
If you have any questions,suggestions,bug-reports,comment or even just to say that you like this program

send me e-mail at:

    FFaure2@aol.com

    Fabrice Faure