jeffreyhsu2009
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Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.

A (5 square root 2, 225°), (-5 square root 2, 45°)

B (5 square root 2, 315°), (-5 square root 2, 135°)

C (5 square root 2, 135°), (-5 square root 2, 315°)

D (5 square root 2, 45°), (-5 square root 2, 225°)

Respuesta :

Answer:

 the answer is B (5 square root 2, 315°), (-5 square root 2, 135°)

Step-by-step explanation:

1) Let A be the point (x, y) = (5, - 5)  

=> x = 5 and y = - 5  

r = √(x² + y²) = √(25 + 25) = √50 = ± 5√2  

tan Θ = - 5/5 = - 1  

=> Θ = (i) 315º or - 45º ; (ii) 135º or - 225  

Hence, the Polar Coordinates of A are (i) (5√2, 315º) (ii) (- 5√2, 135º)

Two pairs of polar coordinates for the point is option b,

Calculation of two pairs:

Here we assume that A be the point (x, y) = (5, - 5)  

So,

x = 5 and y = - 5  

Now

[tex]r = \sqrt(x^2 + y^2) = \sqrt(25 + 25) = \sqrt50 = \pm 5\sqrt2[/tex]

tan Θ = - 5/5 = - 1  

Now

(i) 315º or - 45º ; (ii) 135º or - 225  

So, the polar coordinates should be (5 square root 2, 315°), (-5 square root 2, 135°)

learn more about the point here: https://brainly.com/question/24598035

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