Leo asked in Science & MathematicsMathematics · 2 months ago

How do I find tan(𝜃) + sin(𝜃) for the angle 𝜃?.?

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5 Answers

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  • ?
    Lv 7
    2 months ago

    The length of the hypotenuse

    h=sqr(9^2+5^2)=sqr(106)

    =>

    tan(theta)+sin(theta)

    =

    5/9+5/sqr(106)

    =

    1.041198487

    approximately.

  • ?
    Lv 7
    2 months ago

    tan(𝜃) + sin(𝜃) 

    = 5/9 + 5/sqrt 106 

    = 1.0411984867341877

  • tan(t) + sin(t) =>

    tan(t) + 1/csc(t) =>

    tan(t) + 1/sqrt(csc(t)^2) =>

    tan(t) + 1/sqrt(1 + cot(t)^2) =>

    (5/9) + 1/sqrt(1 + (9/5)^2) =>

    (5/9) + 1/sqrt(1 + 81/25) =>

    (5/9) + 1/sqrt((25 + 81)/25) =>

    (5/9) + sqrt(25/(25 + 81)) =>

    (5/9) + sqrt(25/106) =>

    (5/9) + 5/sqrt(106) =>

    (5/9) + 5 * sqrt(106) / 106 =>

    (5 * 106 + 5 * 9 * sqrt(106)) / (9 * 106) =>

    5 * (106 + 9 * sqrt(106)) / 954 =>

    5 * (9 + sqrt(106)) * sqrt(106) / 954

  • 2 months ago

    Remember the SOH-CAH-TOA mnemonic:

    SOH --> Sin(θ) = Opposite/Hypotenuse

    CAH --> Cos(θ) = Adjacent/Hypotenuse

    TOA --> Tan(θ) = Opposite/Adjacent

    In your picture you have the Opposite side (5) and the Adjacent side (9), so tan(θ) is really easy.

    tan(θ) = 5/9

    For sin(θ) you need the hypotenuse. Do you remember the Pythagorean Theorem?

    a² + o² = h²

    9² + 5² = h²

    81 + 25 = h²

    106 = h²

    h = √106

    Now can *you* find an expression for sin(θ)? Add them together.

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  • rotchm
    Lv 7
    2 months ago

    Hint: What is tan(theta) here? [they gave it to you]. 

    Answer that then we will take it from there.

    Hopefully no one will spoil you the answer. That would be very irresponsible of them. 

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