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# Polar Coordinates Help

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Let $A, B, C,$ and $D$ be the points below.  The points $A, B, C, D$ have polar coordinates $(4, 1), (4, -7), (-4, -9), (4, 2)$ in some order, where the angles are in radians. Order$A, B, C, D$to match the polar coordinates below.

I don't understand how to find the angles the points may be at.  Is there an equation for $\theta$ where the values return $1, -7, -9,$ and $2$?  I get they are all equidistant because |r|=4.  Could someone please help or give me a hint?  Thank you in advanced

Feb 16, 2023

#2
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Perhaps it's easier to see in degrees:

-7 radians = -401.1 degrees  This has rotated clockwise by more than 360 degrees.  How much more?  -41.1  So it's in the fourth quadrant.

-9 radians = -515.7 degrees.  This has also rotated clockwise by more than 360 degrees.  How much more?  -155.7.  This place it in the third quadrant, which doesn't match any of the points on your diagram!

Feb 16, 2023
#3
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Ohhhhh I see. I'm so used to seeing radians with $\pi$ I totally forgot. Thank you!  Also, the -9 works for C because it's going the opposite direction of -155,7 degrees (r=-4).  Thank you so much again

Saphia1123  Feb 16, 2023