Edytujesz „Równanie trygonometryczne”

Z Nonsensopedii, polskiej encyklopedii humoru

Uwaga: Nie jesteś zalogowany. Jeśli wykonasz jakąkolwiek zmianę, Twój adres IP będzie widoczny publicznie. Jeśli zalogujesz się lub utworzysz konto, Twoje zmiany zostaną przypisane do konta, wraz z innymi korzyściami.

Ta edycja może zostać anulowana. Porównaj ukazane poniżej różnice między wersjami, a następnie zapisz zmiany.

Aktualna wersja Twój tekst
Linia 1: Linia 1:
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'''Równanie trygonometryczne''' – szczególny rodzaj [[Równanie|równania]], w którym oprócz literek i cyferek pojawiają się słówka ''sin'', ''cos'', ''tg'', ''ctg'', ''cosh'' itp.. Równania te zostały wynalezione przez starożytnych Greków w celu dręczenia dzieci objętych obowiązkiem edukacji matematyki.

==Sposób dowodzenia prawdziwości równania trygonometrycznego==
Aby dowieść prawdziwość równania trygonometrycznego, np.:
::''cos (x/n) = sin<sup>2</sup>(x) * &pi;''

należy:

* zapisać lewą i prawą stronę równania w odpowiednio lewy górnym i prawym dolnym rogu kartki
* korzystając z podstawowych praw [[Trygonometria|trygonometrii]] i [[Algebra|algebry]] w sposób dowolny przekształcać i rozwijać równania w następujący sposób:
**jeżeli rozwijamy lewą stronę równania, dopisujemy ''= nowe rozwinięcie'' po prawej stronie ostatniej wartości, lub linijkę niżej po lewej stronie
**jeżeli rozwijamy prawą stronę równania, dopisujemy ''nowe rozwinięcie ='' po lewej stronie ostatniej wartości, lub linijkę wyżej po prawej stronie
* gdy nie już miejsca na dopisanie nowej postaci, stawiamy ''='' łączący oba ciągi
===Przykład===
Udowodnimy, że ''sin(x)=cos(x)'' dla przykładu niewielkiej kartki:<br/>
<math>sin(x) = sin(x) + 1 - 1</math><br/>
<math>cos(x)*(\sqrt{(cos(x)})^{(-2)} + cos(x) = cos(x)</math><br/>
<math>sin(x) = sin(x) + 1 - 1 = \sqrt{cos^2(x) - 1} + (\frac{3\sqrt3}{\sqrt{27}})</math><br/>
<math>cos(x)*(\sqrt{cos(x))^{-2} + cos(x)} = cos(x)</math>
<math>sin(x) = sin(x) + 1 - 1 = \sqrt{cos^2(x) - 1} + (\frac{3\sqrt3}{\sqrt{27}}) = cos(x)*(\sqrt{cos(x)^{(-2)}} + cos(x) = cos(x)</math>

W ten sposób udowodniliśmy, że ''sin(x)=cos(x)''

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{{Matematyka}}

[[Kategoria:Matematyka]]
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