Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

Given csc(theta)=5/4, determine tan(theta) if (pi/2) is < or equal to (theta) < or equal to (pi)?

3 Answers

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  • 4 weeks ago
    Favourite answer

    cosecθ = 1/sinθ

    so, 1/sinθ = 5/4

    i.e. sinθ = 4/5

    As we have a 3, 4, 5 triangle we have that cosθ = -3/5 

    Note: negative, as cosθ < 0 in Qii

    And sinθ/cosθ = tanθ = (4/5)/(-3/5)

    i.e. tanθ = -4/3

    :)>

  • cosmo
    Lv 7
    4 weeks ago

    csc(theta) = 5/4

    sin(theta) = 4/5

    cos(theta) = sqrt(1 - (4/5)^2)  = sqrt(1 - 16/25) = sqrt(9/25) = + or - 3/5

    If theta is in the second quadrant, then cos(theta) = - 3/5

    tan(theta) = sin/cos = (4/5)/(-3/5) = -4/3

  • csc(t)^2 - cot(t)^2 = 1

    cot(t) = 1/tan(t)

    (5/4)^2 - cot(t)^2 = 1

    (5/4)^2 - 1 = cot(t)^2

    25/16 - 16/16 = cot(t)^2

    9/16 = cot(t)^2

    16/9 = tan(t)^2

    +/- 4/3 = tan(t)

    You're in Q2, so is tan(t) positive or negative?  You have a 1-in-2 shot here, just by guessing

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