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5 September, 14:41

Given : cos (θ) = - 4/5 | sin x = - 12/13

Evaluate: cos (θ + x)

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Answers (1)
  1. 5 September, 17:32
    0
    cos (θ + x) is 16/65

    Step-by-step explanation:

    Step 1:

    Given cos θ = - 4/5, find sin θ.

    cos θ = adjacent side/hypotenuse = - 4/5

    The opposite side can be found using Pythagoras Theorem.

    Hypotenuse² = Opposite Side² + Adjacent Side²

    ⇒ Opposite side² = Hypotenuse² - Adjacent Side²

    = 5² - (-4) ² = 25 - 16 = 9

    ∴ Opposite Side = 3

    ⇒ sin θ = opposite side/hypotenuse = 3/5

    Step 2:

    Given sin x = - 12/13, find cos x.

    sin x = opposite side/hypotenuse = - 12/13

    The adjacent side can be found using Pythagoras Theorem.

    Hypotenuse² = Opposite Side² + Adjacent Side²

    ⇒ Adjacent side² = Hypotenuse² - Adjacent Side²

    = 13² - (-12) ² = 169 - 144 = 25

    ∴ Adjacent Side = 5

    ⇒ cos x = adjacent side/hypotenuse = 5/13

    Step 3:

    Find cos (θ + x).

    cos (θ + x) = cos θ cos x - sin θ sin x

    = - 4/5 * 5/13 - 3/5 * - 12/13

    = - 20/65 + 36/65 = 16/65
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