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Math Help - HW Help?

  1. #1
    Junior Member
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    Question HW Help?

    Hey all,
    Could I get some help on how to get the answers for these? I've been trying and I have no idea what I'm doing wrong:

    1)[cos^-1(cos(-5pi/3))]
    I got 2pi/3 since 0< 2pi/3 < pi

    So the answer is 2pi/3?

    2) [sin(x)/cos(-x)] + [sin (-x)/cos(x)]

    Don't know where to start. Probably simpler than I'm making it....

    3) csc[cos^-1(sqrt(2)/3)]

    I got 3sqrt(2)/4

    4) Establish the identity [cot/1-tan] + [tan/1-cot] = 1 + tan + cot

    This one is so messy, basically I got stuck at
    (cos/sin)(1 - cos/sin) + (sin/cos)(1- sin/cos)

    5) Est. the identity cos(α-β)cos(α+β) = cos^2 α - sin^2 β

    I kept foiling this over and over and the last time, I kept getting stuck at


    (cos^2 α cos^2 β) - (sin α sinβ sin α sinβ)


    Any help and explanations would be great, thanks.
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  2. #2
    MHF Contributor
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    1) Try again. What is the "Reference Angle" for -5pi/3?

    2) f(x) = cos(x) is an "Even Function"
    2) h(x) = sin(x) is an "Odd Function"
    2) What properties have odd and even functions?

    3) No good. How did you get that?

    That's enough of that. Please show your work and we can get started on setting you in the right direction.

    5) I was going to gove it a rest, but then I saw "foil". Please forget you ever saw that term. Just learn to multiply.

    cos(a-b) = cos(a)cos(b)+sin(a)sin(b)
    cos(a+b) = cos(a)cos(b)-sin(a)sin(b)

    Rather than try to work with all of this...

    A = cos(a)cos(b)
    B = sin(a)sin(b)

    This gives...

    cos(a-b) = A+B
    cos(a+b) = A-B

    Now what?
    Last edited by TKHunny; July 24th 2010 at 08:59 PM. Reason: Picking on "FOIL".
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  3. #3
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    #1) "Find the exact value."
    -5\pi/3 + 3\pi/3 = -2\pi/3
    -2\pi/3 + 3\pi/3 = \pi/3?


    #2) "Simplify the expression."
    [sin(x)/cos(x)] - [sin(x)/cos(x)]
    tan(x) - tan(x)
    0?

    #3) "Find the exact value."

    I got 3 sqrt(2)/4 by:
    x^2+y^2=r^2
    (1^2)+y^2=3^2

    1+y^2=r^2
    y= 8 = 2 sqrt2
    csc = r/y = 3/2sqrt2 = 3sqrt2/4?
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  4. #4
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    1) Excellent. Now what?
    2) Very good. Why do you doubt?
    3) ?? What happened to the sqrt(2)? You had one when you started. It seems to have disappeared.
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