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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
up vote 1 down vote accepted

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 $ enter image description here

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This works, of course, I had a rounding issue and needed to convert to radians. – RBZ Jun 12 '12 at 21:11

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