YarelliD154766 YarelliD154766
  • 03-11-2022
  • Mathematics
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Which set of polar coordinates names the same point as (-5.5) ? ZT O O A. (5, O B. (5:59) O 5 57 4 377 O c. -5 O D. 7T 5. )

Which set of polar coordinates names the same point as 55 ZT O O A 5 O B 559 O 5 57 4 377 O c 5 O D 7T 5 class=

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RamonaF252309 RamonaF252309
  • 03-11-2022

Recall that the following points represent the same point as the point (x,θ)

[tex]\begin{gathered} (-x,\theta+\pi), \\ (-x,\theta-\pi), \\ (x,\theta+2n\pi)\text{.} \end{gathered}[/tex]

Now, notice that:

[tex]\frac{5\pi}{4}=\frac{4\pi}{4}+\frac{\pi}{4}=\pi+\frac{\pi}{4}\text{.}[/tex]

Therefore, the point:

[tex](5,\frac{5\pi}{4})[/tex]

represent the same point as the point

[tex](-5,\frac{\pi}{4})\text{.}[/tex]

Answer: Option B.

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