Question

MEDAL!

Answer 1

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

Answer 2

@ganeshie8

Answer 3

"Polar coordinates are in the form (r, Θ). First we need to compute compute r. Since (x, y) = (5, -5) is the endpoint of the hypotenuse of the reference triangle, and the distance from (0, 0) to (5, -5) is length r, then we get the following:

x² + y² = r²
(5)² + (-5)² = r²
25 + 25 = r²
50 = r²
√50 = r
5√2 = r.

Now we need to determine Θ:

y/x = sin Θ / cos Θ
y/x = tan Θ
-5/5 = tan Θ
-1 = tan Θ
Θ = arctan (-1).

Recall that r² = (-r)². So r can point in the positive direction, or the diametrically opposite negative direction. Consequently, using a calculator to look up arctan (-1), we get this:

Θ = arctan (-1) = 315°, and Θ = arctan (-1) = (315° - 180°) = 135°.

So the two pairs of coordinates are (5√2, 315°), and (5√2, 135°)."