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25 June, 09:15

If sin theta=-3/5 and cos theta>0, what is the value of tan theta?

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

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Answers (2)
  1. 25 June, 09:24
    0
    The answer to your question is the second choice tan Ф = - 3/4

    Step-by-step explanation:

    Data

    sin Ф = - 3/5

    cos Ф > 0

    Process

    1. - The sin Ф is negative, which means that is in the third or fourth quadrant.

    2. - sin Ф = - 3/5 and sin Ф = Opposite side/hypotenuse

    then, Opposite side = 3 hypotenuse = 5

    3. - Calculate the adjacent side using the Pythagorean theorem

    c² = a² + b²

    b² = c² - a²

    b² = 25 - 9

    b² = 16

    b = 4

    4. - If cos Ф is in the third quadrant

    cos Ф = - 4/5 and cos Ф < 0 This is incorrect

    5. - If cos Ф is in the fourth quadrant

    cos Ф = 4/5 and cos Ф > 0 This is correct

    Then, this angle is in the fourth quadrant

    6. - Calculate tan Ф

    tan Ф = - 3/4
  2. 25 June, 09:33
    0
    option b

    Step-by-step explanation:

    Consider a right angled triangle ABC

    BI/

    I /

    I /

    AI__/C

    let theta be at angle C

    sin theta=-3/5 (opposite/hypotenuese)

    AB²+AC²=BC#

    9+AC²=25

    AC=√16=4

    hence

    tan theta = - 3/4 (opposite/adjacent)
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