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Math Help - Differentiating sin functions

  1. #1
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    Differentiating sin functions

    Not sure how to differentiate these functions, if you could show the steps for either function that'd be great .

    Sorry I also don't know how to format it correctly so bear with me.

    Question:
     <br />
p(t) = 70sin((2pi/10)t) +120<br /> <br />
    at t = 6

    and

     <br />
P(t) = 3sin(theta -(pi/2)) <br />

    at theta = pi/3

    Thanks!
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  2. #2
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     (\sin nt)' = n\cos nt

    Also

     (\sin (\theta +n))' = \cos \theta by the chain rule.
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  3. #3
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    I can't seem to make the second one work.
    This is what I did;
    3sin(x-pi/6) becomes
    3cos(x-pi/6)*(1)

    Whats wrong with that?

    The answer is supposed to be 0.05 but i keep getting 2.99.
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  4. #4
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    By the chain rule

     y= \sin (\theta +n)

    Make  u=\theta +n\implies y = \sin u

    Now find \displaystyle \frac{dy}{d\theta} = \frac{du}{d\theta}\times \frac{dy}{du}
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  5. #5
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    I'm still confused, would you be able to show me the next step and then maybe I'll understand?
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  6. #6
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    It seems your attempt is fine. In post #2 I should've written \cos(\theta +n)

    \displaystyle \frac{dy}{du} = \cos u

    \displaystyle \frac{du}{d\theta} = 1
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  7. #7
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    Alright, so then it will be y' = 3*cos(pi/3-pi/6) which leaves me at 2.59
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