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I'm trying to figure this out for player movement in a video game but I'm having trouble figuring it out: How do I find a point $(x_1,y_1)$ if I have an origin point $(x_0,y_0)$, a distance, and $\theta$?

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Voted to close....... – user9413 Jun 11 '11 at 16:38
What is $\theta$ relative to? The $x$-axis, the $y$-axis, clockwise, anticlockwise...? – Rahul Jun 11 '11 at 17:28
x axis, counter clockwise – Xavier Jun 11 '11 at 17:38

Use the following formulas: $$ x_1 = x_0 + d\cos\theta\qquad\text{and}\qquad y_1=y_0 + d\sin\theta. $$

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Thank you. Do these formulas have a name or something I can use to reference them by? – Xavier Jun 11 '11 at 16:58
@Xavier: If the origin is at (0,0), the point at distance $r$ and angle $\theta$ is at $(r\cos\theta, r\sin\theta)$. This can perhaps be called changing from polar coordinates to rectangular coordinates. Taking the origin at $(x_0,y_0)$ instead is just a translation. – ShreevatsaR Jun 11 '11 at 19:02

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