trig

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find the exact values of THE SIX TRIGONOMETRIC FUNCTIONS OF THE ANGLE THETA WHICH HAS A POINT ON THE TERMINAL SIDE OF (-1,4)

  • trig -

    plot (0,0), (-1,0), (0,4) and connect the dots

    http://www.mathsisfun.com/sine-cosine-tangent.html

  • trig -

    (0 , 0), (-1 , 4).

    X = -1 - 0 = -1.

    Y = 4 - 0 = 4.

    r^2 = X^2 + Y^2,
    r^2 = (-1)^2 + 4^2 = 17,
    r = sqrt(17).

    sin(Theta) = Y/r = 4 / sqrt(17) =
    4*sqrt(17) / 17.

    cos(Theta) = X/r = -1/sqrt(17) =
    -1*sqrt(17) / 17.

    tan(Theta) = Y/X = 4 / -1 = -4.

    csc(Theta) = 1/sin(Theta) = 17 / 4*sqrt(17) = 17*sqrt(17) / 4*17 =
    sqrt(17) / 4.

    sec(Theta) = r/X = 1/cos(Theta) =
    17 / -1*sqrt(17) = -17*sqrt(17) / 17
    = -1*sqrt(17).

    cot(Theta) = 1/tan(Theta) = X/Y =
    -1/4 = -(1/4).

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