Si: Tg θ =√2 ∧ θ es agudo √7 Calcular: A = 3(Sen θ + Cos θ) – √7

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Si: Tg θ =√2 ∧ θ es agudo √7 Calcular: A = 3(Sen θ + Cos θ) – √7

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Nguyệt Ánh 5 years 2021-08-28T15:47:47+00:00 1 Answers 17 views 0

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  1. thienthi
    0
    2021-08-28T15:49:02+00:00
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    Answer:

    A \approx 1.488

    Step-by-step explanation:

    Por definición de razones trigonométricas, tenemos las siguientes identidades:

    \tan \theta = \frac{y}{x} = \sqrt{2} (1)

    \sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}} (2)

    \cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}} (3)

    Si \theta es agudo, entonces x, y > 0.

    De (1), suponemos x = 1 que y = \sqrt{2}, entonces los valores de las funciones seno y coseno:

    \sin \theta = \frac{\sqrt{2}}{\sqrt{5}} = \sqrt{\frac{2}{5} }

    \sin \theta = \frac{\sqrt{10}}{5 }

    \cos \theta = \sqrt{\frac{1}{5} }

    \cos \theta = \frac{\sqrt{5}}{5}

    Por último, calculemos A:

    A = 3\cdot \left(\frac{\sqrt{10}}{5} + \frac{\sqrt{5}}{5} \right) - \sqrt{7}

    A \approx 1.488

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