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Math Help - Two little questions relating to pi

  1. #1
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    Two little questions relating to pi

    I have just finished doing and marking a past paper. I did pretty well but there are two little 3-mark questions which I struggled with:

    Question 1
    Given that arcsinx = π/6, find x. Find arccosx in terms of π.

    Question 2
    The curve y = xsin3x crosses the x-axis at P. Find the x-coordinate of P.

    According to the examiner's report both of these questions were meant to be simple but quite a few people couldn't understand them. So I would really appreciate if someone could explain in detail how to do each of these questions.

    Much Thanx
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  2. #2
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    Quote Originally Posted by hopingforhelp View Post
    Question 1
    Given that arcsinx = π/6, find x. Find arccosx in terms of π.
    x would be 1/2 because the sin (π/6) = 1/2. So now, to find arccos (1/2) you need the angle whose cosine is 1/2. The angle would be π/3.


    01
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  3. #3
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    Thanx yeongil but could you please explain why the process involves finding sin (π/6), when the question says arcsinx = π/6, thats the part that confused me when I checked the markscheme.
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  4. #4
    MHF Contributor Amer's Avatar
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    arcsinx=sin^{-1}x

    sin^{-1}x=\frac{\pi}{6}

    sin(sin^{-1}x)=sin(\frac{\pi}{6})

    x=sin(\frac{\pi}{6})=\frac{1}{2}


    Question 2
    The curve y = xsin3x crosses the x-axis at P. Find the x-coordinate of P.
    crosses x-axis when y=0 right
    so

    xsin(3x)=0

    x=0....and...3x=n\pi....x=\frac{n\pi}{3}...n... in...N.."natural"
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  5. #5
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    Thanx Amer question 1 seems really clear to me now. However for question 2 I have no idea what natural means or does, pls could you explain further. Thanx
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  6. #6
    MHF Contributor Amer's Avatar
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    I mean natural number 1,2,3,4,5,6,.. and so on

    cuz sin3x=0

    3x=n\pi


    sin(0)=0,sin\pi=0,sin2\pi=0,sin3\pi=0,sin4\pi=0...  .and... so... on
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  7. #7
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    Sorry for being slow to catch on but why does 3x = nπ instead of equalling zero?
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  8. #8
    MHF Contributor Amer's Avatar
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    because 3x=n\pi

    contain your solution just sub zero instead of n because sinx=0 have infinite solutions
    0,\pi,2\pi,3\pi,4\pi,5\pi......

    so to take all solutions I said

    3x=n\pi this inclusive all solutions for sin3x=0

    that's it

    it is clear or not ....
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  9. #9
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    Thanx Amer, I think I understand now
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