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Math Help - Any help getting me started solving these constants would be appreciated:

  1. #1
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    Any help getting me started solving these constants would be appreciated:

    Find the real positive constants C and F for all real t such that:

    2.5cos(3t) - 1.5sin(3t+pi/3) = Ccos(3t+F)
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  2. #2
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    Why not just solve for F in terms of C and t. Note C will get in the denominator so will have c\ne 0 and also an \arccos in there and I think a 2\pi multiple also.
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  3. #3
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    Quote Originally Posted by Casiofx115 View Post
    Find the real positive constants C and F for all real t such that:

    2.5cos(3t) - 1.5sin(3t+pi/3) = Ccos(3t+F)
    Hi

    Expand sin(3t+pi/3)
    Group the terms in cos(3t) and use a cos(3t) + b sin(3t) = \sqrt{a^2+b^2}\:\cos(3t+F)
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    Quote Originally Posted by running-gag View Post
    Hi

    Expand sin(3t+pi/3)
    Group the terms in cos(3t) and use a cos(3t) + b sin(3t) = \sqrt{a^2+b^2}\:\cos(3t+F)
    Can you elaborate a bit more please? I am not sure how to "expand" sin(3t+pi/3) ...
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  5. #5
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    Quote Originally Posted by Casiofx115 View Post
    Can you elaborate a bit more please? I am not sure how to "expand" sin(3t+pi/3) ...
    Your post title was Any help getting me started solving these constants would be appreciated

    You've been given that start. Now it's your turn to show some working. It's assumed you're familar with the compound angle formula for expanding sin (x + y) .... (if not, then I don't see why you'd be given a question like this to solve in the first place).
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    Quote Originally Posted by mr fantastic View Post
    Your post title was Any help getting me started solving these constants would be appreciated

    You've been given that start. Now it's your turn to show some working. It's assumed you're familar with the compound angle formula for expanding sin (x + y) .... (if not, then I don't see why you'd be given a question like this to solve in the first place).
    Yes, you'd think after four years of engineering school this sort of thing would be old hat for me but I've never really cared much for doing math for the sake of doing math.

    Thanks for the tip on expanding with the sum/difference formulas.

    Next question: I can see in the previous that solving for coefficients "a" and "b" would net me coefficient "C", but I'm not exactly sure where that comes from. I mean, I know that sin^2(3t) + cos^2(3t) = 1, but how does asin(3t) + bcos(3t) = Ccos(3t+F) ?? and wouldn't the fact that "F" is in the parenthesis mess it up?



    BTW, you misspelled familar(sic).
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  7. #7
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    Okay, here's the best I can do on this for today. Can one of you look at it and tell me where I'm wrong please ...
    Attached Thumbnails Attached Thumbnails Any help getting me started solving these constants would be appreciated:-lastscan.jpg  
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  8. #8
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    Quote Originally Posted by Casiofx115 View Post
    Yes, you'd think after four years of engineering school this sort of thing would be old hat for me but I've never really cared much for doing math for the sake of doing math.

    Thanks for the tip on expanding with the sum/difference formulas.

    Next question: I can see in the previous that solving for coefficients "a" and "b" would net me coefficient "C", but I'm not exactly sure where that comes from. I mean, I know that sin^2(3t) + cos^2(3t) = 1, but how does asin(3t) + bcos(3t) = Ccos(3t+F) ?? and wouldn't the fact that "F" is in the parenthesis mess it up?



    BTW, you misspelled familar(sic).
    Expand the left hand side of the given equation using the compound angle formula. Expand the right hand side using the compound formula. Equate the coefficients of cos(3t) and sin(3t) on each side. Do all this and you will get the following two equations:

    \frac{10 - 3 \sqrt{3}}{4} = C \cos F .... (1)

    \frac{3}{4} = C \sin F .... (2)

    After 4 years of engineering school (which I'll assume included the odd maths course along the way) you should be familir with how to solve these two equations simultaneously (which you should carefully check).


    Edit: I only just saw your above post but don't have time to review it right now.
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  9. #9
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    Quote Originally Posted by Casiofx115 View Post
    Find the real positive constants C and F for all real t such that:

    <br />
\frac{5}{2}\cos(3t) - \frac{3}{2}\sin(3t+\frac{\pi}{3}) = C\cos(3t+F)<br />
    Since your purpose is to find the constants  C and  F for all real  t . Then you can pick any  t and put it into your equation.

    For example, let  3t=0 , you get:
    <br />
\frac{5}{2} - \frac{3}{2}\times \frac{\sqrt{3}}{2} = C\cos F<br />

    - Let  3t=-\frac{\pi}{2} , you get:
    <br />
\frac{3}{2} \times \frac{1}{2} = C\sin F<br />
    Last edited by mr fantastic; September 18th 2009 at 09:37 AM. Reason: Restored original reply
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  10. #10
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    Quote Originally Posted by luobo View Post
    Since your purpose is to find the constants  C and  F for all real  t . Then you can pick any  t and put it into your equation.

    For example, let  3t=0 , you get:
    <br />
\frac{5}{2} - \frac{3}{2}\times \frac{\sqrt{3}}{2} = C\cos F<br />

    Let  3t=-\frac{\pi}{2} , you get:
    <br />
\frac{3}{2} \times \frac{1}{2} = C\sin F<br />
    I have to thank you for this ... eloquent!

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