precal

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use the given info. to find the exact value of the trig function.

csc u=-6/5, tan u is greater than 0
Find cos u/2

  • precal -

    csc u = -6/5
    sinu = -5/6
    by Pythagoras, and knowing sin u is negative and tan u is positive
    cosu = -√11/6

    we know cosA = 1 - 2cos^2(A/2)
    or
    cosu = 1 - 2cos^2(u/2)
    -√11/6 = 1 - 2cos^2(u/2)
    2cos^2(u/2) = 1 + √11/6)
    cos u/2 = √[(1 + √11/6)/2]

    check my arithmetic,

  • precal -

    can u simplify the answer any more?????

  • Correction - precal -

    I had the formula backwards, ...
    Should have been

    cos A = 2cos^2(A/2) - 1
    or
    cos u = 2cos^2 (u/2) - 1
    -√11/6 + 1 = 2cos^2 (u/2)
    -√[1 - √11/6)/2] = cos (u/2)

    I picked the negative value, since we knew u was in III, so u/2 was in II, and in II the cosine is negative.

    Since you wanted the "exact" value, there is no point simplifying the above answer.

  • precal -

    thank u

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