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Math Help - I don't get how to do this >_<

  1. #1
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    I don't get how to do this >_<

    Another question about differentiating a trigonometric function except I was away when they taught how to do it and I really am very bad at it.

    a) Find the equation of the tangent to the curve y = sinx at the origin

    I know this should be pretty straight foward but as I said I'm really bad at this kind of stuff.

    b) Using a graph or otherwise, state the number of solutions to the equation sinx = x

    c) Let m be a positive number. For what set of values does the equation sinx = mx have exactly 3 solutions satisfying
    -π ≤ x ≤ π
    [I'm not sure if this is only my computer but those signs there on the last line should be pi's because on my computer some weird symbol is coming up]
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by sweetG View Post
    Another question about differentiating a trigonometric function except I was away when they taught how to do it and I really am very bad at it.

    a) Find the equation of the tangent to the curve y = sinx at the origin

    I know this should be pretty straight foward but as I said I'm really bad at this kind of stuff.
    The equation of the tangent to the curve of a function f at a point a is y=f(a)+(x-a)f'(a). In your case, a=0 (origin) and f(x)=\sin x hence the equation of the tangent you're looking for is y=\sin 0+(x-0)\sin '(0)=\ldots

    b) Using a graph or otherwise, state the number of solutions to the equation sinx = x
    Using a graph is a good idea. The solutions of \sin x =x are the intersection points of the curves of the two functions x\mapsto x and x\mapsto \sin x. How many such point(s) can you find ?

    [I'm not sure if this is only my computer but those signs there on the last line should be pi's because on my computer some weird symbol is coming up]
    I see the symbol \pi.
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  3. #3
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    Hi,

    given function is y=sinx

    diff with respect to x
    dy/dx=cosx
    dy/dx at (0,0) = cos0=0

    now, we have to find the equation of the tangent formula is (y-y1)=dy/dx(x-x1)
    since x1=0 and y1=0
    plug all the values in the above formula

    y-0=0(x-0)

    your answer is y=0

    ---Rk
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  4. #4
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    Thanks I got the first bit but I'm still very confused about the two last bits (b) and (c). Does anyone know how to do them ?
    By the way 'm' is tangent.
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  5. #5
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by sweetG View Post
    Thanks I got the first bit but I'm still very confused about the two last bits (b) and (c). Does anyone know how to do them ?
    Why are you confused about the second question ? Did you sketch the graph of the two functions ?
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  6. #6
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    Am I supposed to sketch y = sinx and y = x ? Because if so then wouldn't they intersect at many points ?! =S I'm so confused
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  7. #7
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    Sorry guys I made a mistake for part (b), it hits x = 0, x = π and x = - π, right ?

    Hmm not sure what to do for part (c) though.
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  8. #8
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by sweetG View Post
    Am I supposed to sketch y = sinx and y = x ? Because if so then wouldn't they intersect at many points ?! =S I'm so confused
    No, there is only one intersection point.

    Quote Originally Posted by sweetG View Post
    Sorry guys I made a mistake for part (b), it hits x = 0, x = π and x = - π, right ?
    No. \sin \pi =0\neq \pi. Again, did you sketch the graph of the two functions ? If you did, why did you find the solutions x=\pm\pi ? (there is no intersection point for x=\pi )

    Hmm not sure what to do for part (c) though.
    Quote Originally Posted by sweetG View Post
    c) Let m be a positive number. For what set of values does the equation sinx = mx have exactly 3 solutions satisfying [/B] -π ≤ x ≤ π
    I suggest you sketch the graphs of x\mapsto \sin x and of  x\mapsto mx for several values of m. (say m=4,\,m=2,\,m=1,\,m=1/2,\,m=1/4,\,m=1/10\ldots) Using this you should be able to find for which values of m the equation \sin x=mx has exactly three solutions in [-\pi:\pi]. (the answer is an interval, for m sufficiently small, \sin x=mx has always three solutions in [-\pi,\pi])
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