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 swm06 April 13th, 2012 08:51 AM

Polar to Cartesian Coordinate Conversion Help

Convert the following point from a polar to cartesian coordinate.

$(-1,-\frac{3\pi }{4})$

$x= -1\cos(-\frac{3\pi }{4})$= $-1(\frac{1}{\sqrt{2}})$

$x=-\frac{1}{\sqrt{2}}$

$y= -1\sin(-\frac{3\pi }{4})$= $-1(-\frac{1}{\sqrt{2}})$=

$y=\frac{1}{\sqrt{2}}$

$(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$

However this is wrong. Where did I screw up?

 soroban April 13th, 2012 09:32 AM

Re: Polar to Cartesian Coordinate Conversion Help

Hello, swm06!

Quote:
 $\text{Convert to cartesian coordinates: }\:\left(-1,\:-\frac{3\pi }{4}\right)$

$\text{W\!e have: }\:r \,=\,-1,\;\theta \,=\,-\frac{3\pi}{4}$

$x \;=\;r\cos\theta \;=\;(-1)\,\!\cos\left(-\frac{3\pi}{4}\right) \;=\;(-1)\left(-\frac{1}{\sqrt{2}}\right) \;=\;\frac{1}{\sqrt{2}}$

$y \;=\;r\sin\theta \;=\;(-1)\,\!\sin\left(-\frac{3\pi}{4}\right) \;=\;(-1)\left(-\frac{1}{\sqrt{2}}\right) \;=\;\frac{1}{\sqrt{2}}$

$\text{Cartesian coordinates: }\:\left(\frac{1}{\sqrt{2}},\;\frac{1}{\sqrt{2}}\r ight)$

 masters April 13th, 2012 09:34 AM

Re: Polar to Cartesian Coordinate Conversion Help

Quote:
 Originally Posted by swm06 Convert the following point from a polar to cartesian coordinate. $(-1,-\frac{3\pi }{4})$ $x= -1\cos(-\frac{3\pi }{4})$= $-1(\frac{1}{\sqrt{2}})$ $x=-\frac{1}{\sqrt{2}}$ $y= -1\sin(-\frac{3\pi }{4})$= $-1(-\frac{1}{\sqrt{2}})$= $y=\frac{1}{\sqrt{2}}$ My answer: $(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ However this is wrong. Where did I screw up?
Hi swm06,

You missed a sign when you found your x-coordinate. $\cos -\frac{3 \pi}{4}$ is negative. When you multiply by -1, it becomes positive.

$\cos -\frac{3 \pi}{4}=-\frac{1}{\sqrt{2}}$

That will make $x=\frac{1}{\sqrt{2}}$

You should rationalize your denominators in the end to arrive at $$$\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}$$$

[color=#FF0000]A couple of minutes too slow for Soroban![/color]

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