Benedict Pfannerstill
Oct 18, 2024
Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°?
I need assistance with a problem related to polar coordinates. Specifically, I am trying to determine two pairs of polar coordinates for the point (5, -5) within the range of 0° ≤ θ < 360°. The answer choices provided are as follows:
1) (5√2, 315°), (-5√2, 135°)
2) (5√2, 45°), (-5√2, 225°)
3) (5√2, 135°), (-5√2, 315°)
4) (5√2, 225°), (-5√2, 45°)
Could someone please help me identify the correct pairs? Thank you!
2 Answers
Since the point lies in the third quadrant
cos(θ) = x/r where r^2 =x^2+y^2 =5^2(-5)^2 =25+25 = 50 , r = sqrt(50) =5sqrt(2)
cos(θ) = x/r =5/5sqrt(2) =1/sqrt(2) = cos(135)
Hence answer is =(5 sqrt2 , 315°), (-5 sqrt2 , 315°)……………….Ans
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