# Thread: Linear Algebra And Unit Circle

1. ## 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.

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

2. ## 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 $-\sin \theta$.