1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivative of a trigonometric function

  1. Oct 4, 2015 #1
    1. The problem statement, all variables and given/known data

    [itex]\frac{d}{dx}7.5sin(\frac{pi}{10}x) [/itex]

    3. The attempt at a solution

    [itex]7.5(\frac{pi}{10})cos(\frac{pi}{10}x)[/itex]

    Maximum: f'(x) = 0

    [itex]7.5(\frac{pi}{10})cos(\frac{pi}{10}x)[/itex] = 0

    [itex]7.5(\frac{pi}{10})cos^{-1}(0)= \frac{pi}{10}x[/itex]

    **[itex] (\frac{pi}{10}\frac{10}{pi})7.5(90) = x[/itex]

    [itex](1)(7.5)(90) = x = 675[/itex]

    To me, this doesn't seem to be nearly the correct answer because it doesn't make sense given the graph of this function:

    [itex]\frac{pi}{10}x= pi[/itex]

    x = 10

    So, the first arch is at x=0 and x = 10,

    so the the maximum of the curve can not be x = 675.

    What am I doing incorrectly in the derivative of the trigonometric function?

    Thank you
     
  2. jcsd
  3. Oct 4, 2015 #2
    Derivation part looks fine.
     
    Last edited: Oct 4, 2015
  4. Oct 4, 2015 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What, exactly, was the question? You only mention differentiating the function but then set that derivative to 0.
    Yes, this is the correct derivative.

    and so [itex]cos(\frac{\pi}{10}x)= 0[/itex]

    No. To solve [itex]Af(x)= B[/itex], you take [itex]f^{-1}(B/A)[/itex], not [itex]Af^{-1}(B)[/itex].

     
  5. Oct 4, 2015 #4
    Hi lep11,

    Thank you. I had a feeling I was running into the issue at solving for x.



    (1) [itex]7.5\frac{π}{10}cos(\frac{π}{10}x)=0[/itex]

    (2) [itex]7.5\frac{π}{10}cos^{-1}(0)= \frac{π}{10}x[/itex] Here is where I was getting stuck. The first thing I noticed, was that I let cos(0) = 90 instead of π/2.

    (3) [itex] 7.5\frac{π}{10}\frac{10}{π}cos(0) = x[/itex]

    (4) [itex]7.5\frac{π}{2} = x = 11.78[/itex] Which is closer to within the interval of the first arch of the function, but not quite where the maximum should be.

    Playing around with the algebra, I finally arrived at an answer that makes sense:

    If I divide the [itex]7.5\frac{π}{10}[/itex] out of the equation first at step (1):

    [itex]7.5\frac{π}{10}cos(\frac{π}{10}x)=0[/itex]

    [itex]cos(\frac{π}{10}x) = 0[/itex]

    [itex]cos(0) = \frac{π}{10}x[/itex]

    [itex]\frac{10}{π}\frac{π}{2} = 5 [/itex] That sounds more like it.


    However, what I don't understand, is how come I have to divide [itex]7.5\frac{π}{10}[/itex] first? In a regular equation, it doesn't matter when you decide to divide both sides by a number, why does it matter in this situation?

    Thank you.
     
    Last edited: Oct 4, 2015
  6. Oct 4, 2015 #5

    Thank you HallsofIvy,

    [itex]7.5\frac{π }{10}Cos(\frac{π}{10}x) = 0[/itex]

    [itex]Cos(\frac{0}{(7.5\frac{π }{10})}) = \frac{π}{10}x[/itex]

    [itex]Cos(0) = \frac{π}{10}x[/itex]

    [itex]\frac{10}{π}Cos(0) = x[/itex]

    [itex]\frac{10}{π}Cos(0) = x[/itex]

    [itex]\frac{10}{π}\frac{π}{2} = x = 5[/itex]!!!


    Thank you. Now that I know how to solve this and that there is a systematic way to approach, I will be looking into why the formula provided does in fact work. Thank you for your guidance :)
     
  7. Oct 4, 2015 #6

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The product of ##\ 7.5\frac{π }{10} \ ## and ##\ \cos(\frac{π}{10}x) \ ## is zero.


    The only way for a product to be zero is for one of the factors to be zero. The only one which can be zero is ##\ \cos(\frac{π}{10}x) \ ## .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Derivative of a trigonometric function
Loading...