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

Saphia1123 Feb 16, 2023

#2**+2 **

Perhaps it's easier to see in degrees:

1 radian = 57.3 degrees

2 radians = 114.6 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!

Alan Feb 16, 2023

#3**+1 **

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