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my dilema

Here is my problem, I know that if when the coordinates and angles are polar I can use:

$x_1 = d \cos(45^\circ) + x_0$

$y_1 = d\sin(45^\circ) + y_0$

But what if my coordinate system works like this? Up/North positive on the $y$-axis is always zero degrees with 90 degrees being positive on the $x$-axis, all angles are taken clockwise relative from zero (up/north)

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Just do a little change of variable. If you have a point $(x,y) = r(\cos \theta, \sin \theta)$ and want the angle $\theta'$ it makes in the clockwise direction with the positive $y$-axis, just write $$ \theta' = \pi/2 - \theta + 2n\pi $$ for $n \in \mathbb{Z}$.

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  • $\begingroup$ What exactly is n? $\endgroup$ – MerrickFox Apr 2 '14 at 21:09
  • $\begingroup$ $n$ is an integer. To give you an idea, think about the angle $\theta=\pi/4$ or $45^\circ$. This is the same thing (in terms of specifying your position) as $45^\circ + 360^\circ$ because if you add $360^\circ$ you've gone around in a circle and come back where you started, right? You could also go around twice, or three times, etc. So $n$ there you can think of being the number of times you went around in a circle. Hope that helps $\endgroup$ – user139388 Apr 2 '14 at 21:12
  • $\begingroup$ I would just like to let you know you helped me a great deal today, I've been struggling with this task today for possibly 7-8 hours straight and have been pulling my hair out. You have provided me with a massive amount of relief with this solution and I would like to thank you for that. :) $\endgroup$ – MerrickFox Apr 3 '14 at 0:17
  • $\begingroup$ Hey, no problem, glad I was helpful. The community here is great for that sort of thing, so feel free to come by any time with more questions. Also, you can show appreciation by accepting the answer, and up-voting if you like. Take care! $\endgroup$ – user139388 Apr 3 '14 at 0:39

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