If sin 𝛼 = − 4/5 and β = 5/3 for a third-quadrant angle 𝛼 and a first-quadrant angle β, find the following.?

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  • ?
    Lv 7
    3 months ago
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    If sin 𝛼 = − 4/5 and sec β = 5/3 for a third-quadrant angle 𝛼 and a first-quadrant angle β, find the following.?

    Cos(beta) = 3/5

    Both reference triangles are 3,4,5. 

    Alpha is in Q3 where sin & cos are both negative. 

    sin(alpha) = -4/5

    cos(alpha) = -3/5

    tan(alpha) = 4/3

    Beta is in Q1 where sin & cos are both positive. 

    sin(beta) = 4/5

    cos(beta) = 3/5

    tan(beta) = 4/3

    sin(alpha+beta) 

    = (-4/5)(3/5) + (-3/5)(4/5)

    = -24/25

    tan(alpha+beta)

    = [(4/3) + (4/3)]/[1-(4/3)(4/3)]

    = (8/3)/(-7/9)

    = -(9*8)/(7*3) = -(3*8)/7 = - 24/7

    for (alpha+beta), sin and tan are both negative. This puts the angle in Q4. 

    /* As to the answer that #45 is a skunk, that is a gross insult to all skunks! */

  • 3 months ago

    Trump is a skunk......🤪

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