Gráfico
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PiR2 :: Matemática :: Trigonometria
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Gráfico
Esboce o gráfico da função f: ℝ → ℝ tal que f(x) = sin(x) + cos(x)
Pensei assim:
f(x)² = [sin(x) + cos(x)]²
f(x)² = sin²(x) + cos²(x) + 2 ∙ sin(x) ∙ cos(x)
f(x) = ± √[sin(2a) + 1]
Sei que não é a melhor forma de fazer, mas tem como definir quando a função vai ser positiva ou negativa?
![Gráfico 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![Gráfico 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)
Pensei assim:
f(x)² = [sin(x) + cos(x)]²
f(x)² = sin²(x) + cos²(x) + 2 ∙ sin(x) ∙ cos(x)
f(x) = ± √[sin(2a) + 1]
Sei que não é a melhor forma de fazer, mas tem como definir quando a função vai ser positiva ou negativa?
Ada Augusta- Jedi
- Mensagens : 214
Data de inscrição : 08/09/2023
Giovana Martins gosta desta mensagem
Re: Gráfico
Boa tarde, Ada.
Primeiramente, um jeito meio "carteado" de esboçar gráficos de funções trigonométricas é montando a tabelinha de valores de f(x) tomando os valores de x tal que x = {0, pi/2, pi, 3pi/2, 2pi}. Como a função é periódica, a partir desses 5 valores você já consegue o traçar o comportamento da função (isto, claro, se a questão não for muito complexa). Aqui você já conseguiria descartar a parte positiva e a parte negativa que não convém de acordo com a manipulação algébrica que você fez. Se houver dúvidas aqui, avise.
Ao fazer a manipulação algébrica que você fez, você acabou transformando a função principal em uma função definida por sentenças.
Um outro jeito utilizando Prostaférese:
\[\mathrm{f(x)=sin(x)+cos(x)=cos\left ( \frac{\pi}{2}-x \right )+cos(x)=2cos\left ( \frac{\pi}{4} \right )cos\left ( \frac{\pi}{4}-x \right )=\sqrt{2}cos\left ( \frac{\pi}{4}-x \right )}\]
Prostaférese é a forma padronizada para a resolução de problemas que envolvem somas de senos e cossenos. Ao transformar a soma da questão em um produto, recaímos em uma função trigonométrica padrão do tipo f(x) = a + bcos(cx - d) para montarmos o gráfico.
Se houver dúvidas, avise.
Giovana Martins- Grande Mestre
- Mensagens : 8130
Data de inscrição : 15/05/2015
Idade : 23
Localização : São Paulo
Ada Augusta gosta desta mensagem
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