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Math Help - function question

  1. #1
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    function question

    Let f and g be the functions defined by f(x)=sinx and g(x)=cosx. for which of the following values of a is the tangent line to f at x=a parallel to the tangent line to g at x=a? The answer is 3pi/4 but I dont understand how to get to that...

    How would I go about finding that answer? thanks
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  2. #2
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    Parallel lines have the same slope.
    The derivative determines the slope, so f'(x) = g'(x).
    So for what x does \cos (x) =  - \sin (x)?
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  3. #3
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    what do I use to solve that though? Is there a trig rule that I'm not thinking of that is needed to solve?
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    can anybody point out how I go about solving that?
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  5. #5
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    Quote Originally Posted by jst706 View Post
    can anybody point out how I go about solving that?
    If you really can't see the solution:

    Write this as
    sin(x) = -cos(x)

    \frac{sin(x)}{cos(x)} = -1

    tan(x) = -1

    Can you take it from here?

    -Dan
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  6. #6
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    unfortunately....no...I don't know how to get the x separated from the tan..and then get the pi answer, could you show me and then tell me what these specific rules are called so I can go look them up?
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jst706 View Post
    unfortunately....no...I don't know how to get the x separated from the tan..and then get the pi answer, could you show me and then tell me what these specific rules are called so I can go look them up?
    How can you be given such a question and not have been told how to get the answers??

    Try this site for some basic definitions.

    -Dan
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  8. #8
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    thanks for the site...it was helpful...but tan(x)=-1 so, according to that site x=-45...when converted to radians its says 45 degrees is pi/4 so how would they get 3pi/4? thanks for your help.
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  9. #9
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    Quote Originally Posted by jst706 View Post
    thanks for the site...it was helpful...but tan(x)=-1 so, according to that site x=-45...when converted to radians its says 45 degrees is pi/4 so how would they get 3pi/4? thanks for your help.
    Hello,

    the solution of the equation tan(x) = -1 is not a single value but a set of numbers. There is a main interval where you can find the first solution: \left(-\frac{\pi}{2}, \frac{\pi}{2}  \right)

    \tan(x)=-1~\implies~x=-\frac{\pi}{4}. All other solutions are produced by adding multiples of \pi. That means the next solution is:
    x = -\frac{\pi}{4}+\pi=-\frac{3 \pi}{4}

    I've attached a diagram of the functions f(x) = tan(x) and the line y = -1. The x-coordinate of the intersection points are the solutions of your equation.
    Attached Thumbnails Attached Thumbnails function question-tan_gleich-1.gif  
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