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12 February, 21:23

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

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  1. 12 February, 21:43
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    Hello : sec (θ) = (√26) / 5 and: sin (θ) < 0

    note : sec (θ) = 1/cos (θ)

    so : 1/cos (θ) = (√26) / 5

    cos (θ) = 5/√26

    cos² (θ) + sin² (θ) = 1

    25/26+sin² (θ) = 1

    sin² (θ) = 1/26

    sin (θ) = - (1/√26) ... because : sin θ < 0

    tan (θ) = sin (θ) / cos (θ) = - (1/√26) / 5/√26 = - 1/5
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