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Math Help - Cos sin problem?

  1. #1
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    Cos sin problem?

    Hello. I have a test tomorrow and I'm not sure in one area.

    <\cos \theta, \sin \theta> \cdot <\cos (180+ \theta), \sin(180+ \theta)>

    Explain why the value does not depend on the value of \theta.

    Could someone please talk me through this step by step? thanks.
    Last edited by mr fantastic; February 4th 2009 at 08:51 PM. Reason: Fixed the latex
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by view360 View Post
    Hello. I have a test tomorrow and I'm not sure in one area.

    <\cos \theta, \sin \theta> \cdot <\cos (180+ \theta), \sin(180+ \theta)>

    Explain why the value does not depend on the value of \theta.

    Could someone please talk me through this step by step? thanks.

    here's something you probably never thought of, take the dot product. what do you get?
    Last edited by mr fantastic; February 4th 2009 at 08:52 PM. Reason: Matched quote with edit of OP's post.
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    Quote Originally Posted by Jhevon View Post
    here's something you probably never thought of, take the dot product. what do you get?

    <\cos \theta \cos(180+\theta), \sin \theta \sin(180+ \theta)>
    Last edited by mr fantastic; February 4th 2009 at 09:01 PM. Reason: Fixed the latex
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by view360 View Post
    cos thetacos(180+ theta), sin thetasin(180+ theta)
    that's not the dot product

    \left< a,b \right> \cdot \left< c,d \right> = ac + bd
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    \cos \theta \cos(180+ \theta) + \sin \theta \sin (180+ \theta)?

    btw is this really calc? I'm only a freshman, isn't calc a much more advanced class?
    Last edited by mr fantastic; February 4th 2009 at 08:58 PM. Reason: Fixed the latex
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by view360 View Post
    cos thetacos(180+ theta) + sin thetasin)180+ theta)?
    yes, now recall that \cos (A - B) = \cos A \cos B + \sin A \sin B

    btw is this really calc? I'm only a freshman, isn't calc a much more advanced class?
    yeah, you're right. i was tutoring calc 3 today and we were working with dot products, so my mind automatically filed this under calculus i'll have it changed.
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    Quote Originally Posted by Jhevon View Post
    yes, now recall that \cos (A - B) = \cos A \cos B + \sin A \sin B

    yeah, you're right. i was tutoring calc 3 today and we were working with dot products, so my mind automatically filed this under calculus i'll have it changed.


    Sorry if I sound stupid lol, but i'm not making any connections between the two?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by view360 View Post
    Sorry if I sound stupid lol, but i'm not making any connections between the two?
    replace A with \theta and replace B with 180 + \theta

    do you see it now?
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  9. #9
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    Quote Originally Posted by Jhevon View Post
    replace A with \theta and replace B with 180 + \theta

    do you see it now?
    Oh okay, so it equals cos(A-B), which if you replace it, equals cos(theta-180+theta). So it ends up just equaling cos180, the theta doesn't change that. But why is A = \theta and B 180 + \theta?
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