How do I convert polar coordinates $(10, - \frac{π}{4})$ $(10, -pi/4)$ to rectangular coordinates?

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How do I convert polar coordinates $(10, - \frac{π}{4})$ $(10, -pi/4)$ to rectangular coordinates?

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Answer 1 · 2014-08-14T18:22:39

The answer is $(\sqrt{50}, - \sqrt{50})$ $(sqrt(50), -sqrt(50))$ .

This problem is solved using trigonometry. I like to use the mnemonic SYR, CXR, TYX (pronounced sir kicks'er ticks). $sin θ = \frac{y}{r}, cos θ = \frac{x}{r}, tan θ = \frac{y}{x}$ $sin theta=y/r, cos theta=x/r, tan theta=y/x$ .

So rearranging with algebra, we get $x = r cos θ, y = r sin θ$ $x=r cos theta, y=r sin theta$ .

Next, substitute the polar coordinates. Make sure that your calculator is in RAD mode. However, $\frac{π}{4}$ $pi/4$ is a special angle that you should memorize the ratios.

$x = 10 cos (- \frac{π}{4}), y = 10 sin (- \frac{π}{4})$ $x=10 cos (-pi/4), y=10 sin(-pi/4)$

$- \frac{π}{4}$ $-pi/4$ is in the fourth quadrant, this corresponds with $(\sqrt{50}, - \sqrt{50})$ $(sqrt(50), -sqrt(50))$ .

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How do I convert polar coordinates $(10, - \frac{π}{4})$ $(10, -pi/4)$ to rectangular coordinates?

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