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Latest posts from topic “Identità trigonometrica” Latest posts from topic “Identità trigonometrica” on “ElectroYou”. 2018-02-13T10:43:25Z https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756 Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p756066 PietroBaima 2018-02-13T14:42:17Z 2018-02-13T14:42:17Z
Sempre volentieri. :ok:
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p756063 wall87 2018-02-13T14:31:36Z 2018-02-13T14:31:36Z
[quote="PietroBaima"]In pratica ne calcoli la derivata e vedi che é nulla dappertutto.


Parbleu, avevo chiesto un consiglio trigonometrico, non pensavo di dovermi fare tutto lo studio di funzione :mrgreen:

A parte gli scherzi mi sto ripassando un po di cosine un po alla volta e col poco tempo che ci posso dedicare; è dalle superiori che non faccio questi esercizi, praticamente poco più di una decina d'anni. Alle derivate ci devo ancora ritornare e ora come ora non saprei manco dove pigliarmi, ma quando lo farò sarò felice di tornare sull'argomento.
Intanto ti ringrazio :D
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p756058 PietroBaima 2018-02-13T14:17:20Z 2018-02-13T14:17:20Z
È uno dei miei modi per raccontare una curiositá di mate.

Se devi usare l’analisi allora devi dimostrare che la funzione é costante su tutto il dominio.
In pratica ne calcoli la derivata e vedi che é nulla dappertutto.

Facile, ma... c’è un ma
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p756051 wall87 2018-02-13T14:12:47Z 2018-02-13T14:12:47Z
[quote="PietroBaima"]devo dire che sei “verboso” nei calcoli


Scusa Pietro ma per quanto riguarda i calcoli preferisco fare tutto per bene e una volta sola piuttosto di semplificare troppo e magari perdermi. :ok:

[quote="PietroBaima"]se si dovesse usare l’analisi per dimostrarla, come faresti?

Qui non ho ben capito dove vuoi andare a finire :?
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p756047 PietroBaima 2018-02-13T14:02:24Z 2018-02-13T14:02:24Z
sí, il secondo, ma devo dire che sei “verboso” nei calcoli :-)

ps: se si dovesse usare l’analisi per dimostrarla, come faresti?
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p756040 wall87 2018-02-13T13:54:10Z 2018-02-13T13:54:10Z
Pietro intendi così:

[unparseable or potentially dangerous latex formula]

\frac{1+\tan x}{1-\tan x}\cdot\frac{cos^2x-2\sin x\cos x+\sin^2x}{\cos^2x-\sin^2x}=1

\frac{1+\tan x}{1-\tan x}\cdot\frac{\frac{cos^2x-2\sin x\cos x+\sin^2x}{\cos^2x}}{\frac{\cos^2x-\sin^2x}{\cos^2x}}=1

\frac{1+\tan x}{1-\tan x}\cdot\frac{1-2\tan x+\tan^2x}{1-\tan^2x}=1

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

\frac{1+\tan x}{1-\tan x}\cdot\frac{1-\tan x}{1+\tan x}=1

Forse ripensandoci volevi fare così:

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

e poi di nuovo i calcoli di prima.
Sarà ma secondo me è più sbrigativo quello fatto in [3]; comunque ti ringrazio per gli spunti
interessanti :D
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p756004 PietroBaima 2018-02-13T12:06:02Z 2018-02-13T12:06:02Z
Ahem, certo, volevo dire proprio così... :-"
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p755991 sebago 2018-02-13T11:20:04Z 2018-02-13T11:20:04Z
[quote="PietroBaima"]Dopo aver semplificato, al numeratore hai l’espansione del quadrato del binomio del denominatore.

Probabilmente volevi dire "della differenza di quadrati del denominatore"...
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p755988 PietroBaima 2018-02-13T10:58:00Z 2018-02-13T10:58:00Z
Si può accorciare ancora un po’.

Raccogli un coseno dalla parentesi al numeratore, poi portalo al denominatore.

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

Dopo aver semplificato, al numeratore hai l’espansione del quadrato del binomio della differenza di due quadrati del denominatore. (Grazie Foto Utentesebago)
Re: Identità trigonometrica https://www.electroyou.it/forum/viewtopic.php?f=7&t=72756#p755983 wall87 2018-02-13T10:43:25Z 2018-02-13T10:43:25Z
Intendi così:

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

\frac{1+\tan x}{1-\tan x}\cdot \frac{\cos x-\sin x}{\cos x+\sin x}=1

\frac{1+\tan x}{1-\tan x}\cdot \frac{\frac{\cos x-\sin x}{\cos x}}{\frac{\cos x+\sin x}{\cos x}}=1

\frac{1+\tan x}{1-\tan x}\cdot\frac{1-\tan x}{1+\tan x}=1

In effetti è più veloce :D :ok:
Non mi era venuto in mente, si vede che mi piace complicarmi la vita :mrgreen: