# convert rotation in degrees to percent to move an object x and y directions

So I have been out of school for a very long time and have a forehead slapping question:

$$m = \tan(\theta)$$ where $\theta$ is an angle, but all that gives me is $\frac yx$.

I need to know how far something should move in each vector given that it is pointed at a certain angle.

How is this determined?

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What do you exactly mean by "how far something should move in each vector given that it is pointed at a certain angle"? Seems extremely vague. –  Bouvet Island Jun 12 '12 at 20:00
so I have an object in a x,y plane and I need to know if an object moves forward 10units at 30 degrees [or any angle], how much does the x,y coordinate each change. –  RBZ Jun 12 '12 at 20:02
x changes by $10 \cos 30$ and y changes by $10 \sin 30$ –  Santosh Linkha Jun 12 '12 at 20:17
Seems to work for some angles. I may be looking at a software bug –  RBZ Jun 12 '12 at 20:41

Let's say a point moved for point $(x_1, y_1)$ to $(x_2, y_2)$ , then we know the point has moved $x_2 - x_1$ along x-axis and $y_2 - y_1$ along y-axis.
Given than a point moves $R$ distance along $\theta$ direction, let, $\Delta x$ and $\Delta y$ be the distance moved forward simultaneously on x-axis and y-axis, then we know, $$\Delta x = R \frac {\Delta x}{ R } \text{ ,but } \frac {\Delta x}{ R } = \cos \theta \text{ so we have } \Delta x = R \cos \theta$$
And similarly $\Delta y = R \sin \theta$