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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 (-5.5) ? ZT O O A. (5, O B-example-1
User Nick Daria
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1 Answer

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


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

Now, notice that:


(5\pi)/(4)=(4\pi)/(4)+(\pi)/(4)=\pi+(\pi)/(4)\text{.}

Therefore, the point:


(5,(5\pi)/(4))

represent the same point as the point


(-5,(\pi)/(4))\text{.}

Answer: Option B.

User Shaded
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