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Thread: Linear Algebra And Unit Circle

  1. #1
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    Linear Algebra And Unit Circle

    Watching a video in linear algebra where the author performs a linear transformation to rotate a vector. Everything is making sense to me except the new matrix that has -sin as one of its components (highlighted in blue in the image). Where is that coming from? Perhaps it just has to do with the quadrant we are moving into.

    Linear Algebra And Unit Circle-vector.png

    If you would like to watch the video for reference it is quite short, and this link goes right to it.

    https://youtu.be/DOMg0lXWatM?t=1m25s
    Last edited by lunabell; Sep 13th 2018 at 05:27 PM.
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  2. #2
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    Re: Linear Algebra And Unit Circle

    Yes, it is because you are working in the second quadrant. The angle is an acute angle (from the diagram), so both $\sin \theta$ and $\cos \theta$ are positive. But, you are looking for the point where the $x$-component is negative, which is $-\sin \theta$.
    Last edited by SlipEternal; Sep 13th 2018 at 06:19 PM.
    Thanks from HallsofIvy and lunabell
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