Understanding Polar Coordinates - High School Math

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Question

The polar coordinates of a point are $\left(1.2, \frac{2\pi }{5}\right )$ . Give its -coordinate in the rectangular coordinate system (nearest hundredth).

Answer

Given the polar coordinates $(r,\theta )$ , the -coordinate is $x= r \cos \theta$ . We can find this coordinate by substituting $r = 1.2, \theta = \frac{2\pi }{5}$ :

$x = r \cos \theta = 1.2 \cdot \cos \frac{2\pi }{5} \approx 1.2 \cdot 0.3090 \approx 0.37$

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Question

The polar coordinates of a point are $\left(1.2, \frac{2\pi }{5}\right )$ . Give its -coordinate in the rectangular coordinate system (nearest hundredth).

Answer

Given the polar coordinates $(r,\theta )$ , the -coordinate is $y= r \sin \theta$ . We can find this coordinate by substituting $r = 1.2, \theta = \frac{2\pi }{5}$ :

$y = r \cos \theta = 1.2 \cdot \sin \frac{2\pi }{5} \approx 1.2 \cdot 0.9511 \approx 1.14$

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Question

The polar coordinates of a point are $\left(2.1, \frac{7\pi }{3}\right )$ . Give its -coordinate in the rectangular coordinate system (nearest hundredth).

Answer

Given the polar coordinates $(r,\theta )$ , the -coordinate is $y= r \sin \theta$ . We can find this coordinate by substituting $r = 2.1, \theta = \frac{7\pi }{3}$ :

$y = r \sin \theta = 2.1 \cdot \sin \frac{7\pi }{3} \approx 2.1 \cdot 0.8660 \approx 1.82$

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Question

The polar coordinates of a point are $\left(2.1, \frac{7\pi }{3}\right )$ . Give its -coordinate in the rectangular coordinate system (nearest hundredth).

Answer

Given the polar coordinates $(r,\theta )$ , the -coordinate is $x= r \cos \theta$ . We can find this coordinate by substituting $r = 2.1, \theta = \frac{7\pi }{3}$ :

$x = r \cos \theta = 2.1 \cdot \cos \frac{7\pi }{3} = 2.1 \cdot 0.5 = 1.05$

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