# How do I find this coordinate given the angle and distance from origin.

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)

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 $n \in \mathbb{Z}$.
• $n$ 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 – user139388 Apr 2 '14 at 21:12