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4 August, 05:37

Find tan θ if sec θ = square root of thirty seven divided by six and sin θ < 0.

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Answers (2)
  1. 4 August, 07:52
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    Secθ = sqrt (37) / 6

    is that right?
  2. 4 August, 09:11
    0
    Identity: sec^2 (x) = 1 + tan^2 (x) = > tan^2 (x) = sec^2 (x) - 1

    sec (x) = √[37/6] = > sec^2 (x) = 37/6

    tan^2 (x) = 37/6 - 1 = 31/6

    tan (x) = + / - √[31/6]

    Given that sin (x) is negative and sec (x) is positive, we are in the fourth quadrant, so the tangent is negative, then:

    tan (x) = - √[31/6] = - 2.27
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