# Vector question

1. Dec 14, 2005

### seang

For the vectors in the picture, we're supposed to break down each vector into its x and y components. I dont understand why the x component is given by cos(theta). It seems like it should be sin(theta) to me

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• ###### BilliardBall.png
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2. Dec 14, 2005

### Astronuc

Staff Emeritus
While waiting for approval, let's assume a Cartesian (x,y) coordinate system with x-axis horizontal and y-axis vertical with positive coordinate in upper right quadrant.

Take F to be in the right half, either above or below. If the angle $\theta$ between F and the x-axis, then the component Fx would be given by F cos $\theta$. If however, the angle was taken from the y-axis, then Fx would be given by sin $\theta$.

With respect to F, Fx, Fy, think of F as the hypotenuse of a triangle and Fx and Fy as the legs, and then apply the Pythagorean theorem, i.e. appropriate trigonometric relationship.

3. Dec 14, 2005

### Tide

The x components are gven by the sine of the respective angles in the diagram you showed. Who said otherwise?

4. Dec 14, 2005

### HallsofIvy

The x component of either vector cannot be $sin(\theta)$ or $cos(\theta)$. There is no $\theta$ in the picture!

If, as is often done- but not in this picture, $\theta$ is measured from the positive x-axis, then the x component of the vector would be given by the length of the vector times $cos(\theta)$.

5. Dec 14, 2005

### Astronuc

Staff Emeritus
Last edited: Dec 14, 2005