If x + 6 = 6sin(theta) for 0< theta< pi/2 express cos(2theta) in terms of x?

cos(2theta) =

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  • 1 month ago
    Best Answer

    cos(2theta) = 1 - 2sin^2(theta)

    x + 6 = 6sin(theta)

    sin(theta) = (x + 6) / 6

    sin^2(theta) = (x + 6)^2 / 6^2

    sin^2(theta) = (x^2 + 12x + 36) / 36

    now plug it in

    cos(2theta) = 1 - [ 2(x^2 + 12x + 36) / 36 ]

    cos(2theta) = 1 - (x^2 + 12x + 36) / 18

    But i like this answer better

    cos(2theta) = -(x^2 +12x + 18) / 18

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