trig

FInd the exact value pf the 6 trig function of alpha
Given: point (-2,-6) on the terminal side of the angle in standard position
sin alpha
cos alpha
tan alpha
sec alpha
csc alpha
cot alpha

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  1. (0,0), (-2,-6).

    X = -2-0 = -2.

    Y = -6-0 = -6.

    r = sqrt((-2)^2+(-6)^2) = sqrt40 =
    sqrt(4*10) = 2sqrt10.

    sinA = Y/r = -6/2sqrt10 = -3/sqrt10 =
    -3sqrt10/10.

    cosA = X/r = -2 / 2sqrt10 =
    -1 / sqrt10 = -sqrt10 / 10.

    tanA = Y/X = -6/-2 = 3.

    cscA = 1/sinA = 10 / -3sqrt10 =
    10sqrt10 / -3*10 = 10sqrt10 / -30 =
    sqrt10 / -3.

    secA = 1/cosA = -3 / sqrt10 =
    -3sqrt10 / 10.

    cotA = 1/tanA = 1/3.

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