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It's been ages since i did any coordinate conversions, and typically i have these two which i just can't manage to solve by myself.

  1. I want to express the circle $x^{2}+y^{2}<4, x<0 $

  2. The Area: $x-|y|\ge 0$

For the first problem i just thought it would be as easy as following:

$$0< r < 2$$

$$\frac {\pi}{2}<\theta<\frac{3\pi}{2}$$

For the second problem i don't even know how to begin...

Best Regards

Joe

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2 Answers 2

Maybe this will help you get started. Here's a picture of the region $x-|y|\geq0$:

$\hskip2in$enter image description here

(generated here by Wolfram Alpha). From this picture, there's something you should be able to see immediately: will there be any dependence on $r$? In fact, can you work out what the region is from the picture?

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Thanks for the Quick reply! Allthough i dont think i really understand what you mean by dependency of r. –  user27640 Mar 26 '12 at 6:04
    
You mean the highllighted area i assume. Italien that part om having difficulties expressing in polar cooedinates –  user27640 Mar 26 '12 at 6:08
    
@Joe: I mean, does the question "Is the point $(r,\theta)$ in the region?" depend on what $r$ is? –  Zev Chonoles Mar 26 '12 at 6:10

For the second problem: $-\frac{\pi}{4} \leq \theta \leq \frac{\pi}{4}$ ($x \geq |y|$ hence $x$ is positive, $\cos\theta \geq |\sin\theta|$, from which the inequality for $\theta$ easily follows).

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