Trigonometry

If cot 2(Theta) = 5/12 with 0 (less than or equal to) 2(Theta) (Less than or equal to) Pi, find the cos(Theta), sin(Theta), and tan(Theta).

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  1. cot(2A) = X/Y = 5/12. Q1.
    r^2 = 5^2 + 12^2 = 169
    r = 13.

    cos(2A) = X/r = 5/13.
    sin(2A) = Y/r = 12/13.
    tan(2A) = Y/X = 12/5.

    cos2A = 2cos^2A-1 = 5/13
    2cos^2A = 5/13 + 1 = 18/13
    cos^2A = 18/26
    cosA = sqrt(18/26)
    cosA = 3sqrt(2/26)
    cosA = 3*sqrt(1/13).
    sqrt = Square root.

    sin(2A) = 2sinA*cosA = 12/13.
    2sinA*3sqrt(1/13) = 12/13
    sinA*3sqrt(1/13) = 12/26
    sinA = (12/26)/(3sqrt(1/13)
    sinA = (4/26)/(sqrt(1/13)
    sinA = (2/13)/(sqrt(1/13)
    sinA = (2/13)sqrt(1/13)/(1/13)
    sinA = 2sqrt(1/13).

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