Fundamentos M. E. - Iezzi - Exercício 195
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Fundamentos M. E. - Iezzi - Exercício 195
Relembrando a primeira mensagem :
Estude a variação das seguinte funções reais(Imagem, domínio e período):
[latex]a) f(x) = cos^22x - sen^2x[/latex]
[latex]b) g(x)= \sqrt{3}cosx-senx[/latex]
[latex]c) h(x)= \dfrac{senx + cosx}{cosx-senx}[/latex]
Estude a variação das seguinte funções reais(Imagem, domínio e período):
[latex]a) f(x) = cos^22x - sen^2x[/latex]
[latex]b) g(x)= \sqrt{3}cosx-senx[/latex]
[latex]c) h(x)= \dfrac{senx + cosx}{cosx-senx}[/latex]
Guilherme_003- Iniciante
- Mensagens : 3
Data de inscrição : 25/12/2020
Re: Fundamentos M. E. - Iezzi - Exercício 195
Errei algum cálculo, mas por prostaférese:
sen(x) + cos(x)
sen(x) + sen(π/2 - x)
2 ∙ sen(π/4) ∙ cos(π/4 - x)
√2 ∙ cos(π/4 -x)
cos(x) - sen(x)
sen(π/2 - x) - sen(x)
2 ∙ cos(π/4) ∙ sen(π/4 - x)
√2 ∙ sen(π/4 -x)
[√2 ∙ cos(π/4 -x)] / [√2 ∙ sen(π/4 -x)]
cotg(π/4 -x)
Obrigada pela ajuda, mestre!
sen(x) + cos(x)
sen(x) + sen(π/2 - x)
2 ∙ sen(π/4) ∙ cos(π/4 - x)
√2 ∙ cos(π/4 -x)
cos(x) - sen(x)
sen(π/2 - x) - sen(x)
2 ∙ cos(π/4) ∙ sen(π/4 - x)
√2 ∙ sen(π/4 -x)
[√2 ∙ cos(π/4 -x)] / [√2 ∙ sen(π/4 -x)]
cotg(π/4 -x)
Obrigada pela ajuda, mestre!
Ada Augusta- Jedi
- Mensagens : 214
Data de inscrição : 08/09/2023
Re: Fundamentos M. E. - Iezzi - Exercício 195
Eis o seu erro:
senx + sen(pi/2 - x) = 2.sen[(x + pi/2 - x)/2].cos[(x - pi/2 + x)/2] = 2.sen(pi/4).cos(x - pi/4)] =
= √2.cos(x - pi/4)
Não conferi o outro.
senx + sen(pi/2 - x) = 2.sen[(x + pi/2 - x)/2].cos[(x - pi/2 + x)/2] = 2.sen(pi/4).cos(x - pi/4)] =
= √2.cos(x - pi/4)
Não conferi o outro.
Elcioschin- Grande Mestre
- Mensagens : 72766
Data de inscrição : 15/09/2009
Idade : 78
Localização : Santos/SP
Re: Fundamentos M. E. - Iezzi - Exercício 195
Desculpe não ter visto, não lembro de ter recebido a notificação.
Sobre o erro de conta, eu tinha me referido àquele anterior, na minha primeira pergunta.
De qualquer forma, o meu deu "π/4 -x" porque eu fiz "sen(π/2 - x) +sen(x)" ao invés de "sen(x) + sen(π/2 - x) ". A ordem da soma importa neste caso?
Tinha visto num software e, pelo que vi, não há problemas nem na expressão, nem no gráfico:
![Fundamentos M. E. - Iezzi - Exercício 195 - Página 2 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)
Sobre o erro de conta, eu tinha me referido àquele anterior, na minha primeira pergunta.
De qualquer forma, o meu deu "π/4 -x" porque eu fiz "sen(π/2 - x) +sen(x)" ao invés de "sen(x) + sen(π/2 - x) ". A ordem da soma importa neste caso?
Tinha visto num software e, pelo que vi, não há problemas nem na expressão, nem no gráfico:
Ada Augusta- Jedi
- Mensagens : 214
Data de inscrição : 08/09/2023
Re: Fundamentos M. E. - Iezzi - Exercício 195
Boa noite. Se me permitem, irei dar os meus pitacos. Se eu estiver errada, avisem, por favor.
Élcio, ao inverter a ordem como a colega Ada fez, não irá gerar diferença entre as expressões obtidas, quais sejam: cos(π/4 - x) e cos(x - π/4), tendo em vista a paridade da função cosseno, a qual é par, logo, cos(-x) = cos(x).
A expressão cotg(π/4 - x) obtida a partir das manipulações algébricas via Prostaférese está correta.
E sim, Ada, a expressão da letra C equivale a tan(x + π/4). Veja:
\[\mathrm{f(x)=\frac{sin(x)+cos(x)}{cos(x)-sin(x)}=\frac{\frac{sin(x)}{cos(x)}+1}{1-\frac{sin(x)}{cos(x)}}=\frac{1+tan(x)}{1-tan(x)}=\frac{tan\left(\frac{\pi }{4}\right)+tan(x)}{1-tan\left(\frac{\pi}{4}\right)tan (x)}=tan\left(x+\frac{\pi}{4}\right)}\]
Giovana Martins- Grande Mestre
- Mensagens : 8137
Data de inscrição : 15/05/2015
Idade : 23
Localização : São Paulo
Ada Augusta gosta desta mensagem
Re: Fundamentos M. E. - Iezzi - Exercício 195
Muito obrigada pelos adendos, Giovana.
Eu tinha chegado na expressão e, momentos mais tarde, esqueci como cheguei no resultado
; como deu diferente, supus que estava errado. Mais uma vez, agradeço!
Eu tinha chegado na expressão e, momentos mais tarde, esqueci como cheguei no resultado
![Cool](https://2img.net/i/fa/i/smiles/icon_cool.gif)
Ada Augusta- Jedi
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Data de inscrição : 08/09/2023
Giovana Martins gosta desta mensagem
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