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14 October, 05:40

If cos theta 4/5 and theta lies in quadrant 2, what is the value of tan theta?

1) 3/4 2) 4/3 3) - 3/4 4) - 4/3

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Answers (2)
  1. 14 October, 08:50
    0
    The answer to your question is the third choice - 3/4

    Step-by-step explanation:

    Data

    cos Ф = 4/5

    second quadrant

    Process

    1. - In the second quadrant cosФ is negative.

    2. - cosФ relates the adjacent side and the hypotenuse

    cos Ф = adjacent side / hypotenuse

    Then, Adjacent side = 4 hypotenuse = 5

    3. - Calculate the Opposite side using the Pythagorean theorem

    c² = a² + b²

    5² = 4² + b²

    25 = 16 + b²

    b² = 25 - 16

    b² = 9

    b = 3

    Opposite side = 9

    4. - The tangent relates the Opposite side and the Adjacent side

    tan Ф = Opposite side/Adjacent side

    tan Ф = 3/4

    but it is negative in the second quadrant

    tan Ф = - 3/4
  2. 14 October, 08:55
    0
    Step-by-step explanation:

    since theta is in second quadrant tan value is negative

    COS is 4/5 (adjacent/hypotenuese)

    (adj) ² + (opposite) ² = (hypo) ²

    4² + (opposite) ²=5²

    opposite side=√9=3

    tan thet=3/4

    but theta is in second quadrant

    hence

    tan theta = - 3/4
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