(2√2 , 225°), (2√2 , 45°)
(2√2 , 135°), (2√2 , 315°)
(2√2 , 315°), (2√2 , 135°)
(2√2 , 45°), (2√2 , 225°)
3 Answers

given: point (x = 2, y = 2) with 0° ≤ θ < 360°
polar coordinate equations:
x = r cos(θ)
y = r sin(θ)
or
2 = r cos(θ)
2 = r sin(θ)
dividing we have
tan(θ) = r sin(θ) / (r cos(θ)) = 2 / 2 = 1
or θ = 315
hence to find the radius r
2 = r cos(θ)
2 = r cos(45)
r = 2 / cos(45)
r = 2 / (1 / sqrt(2))
r = 2 sqrt(2)
hence one point is:
(r = 2 sqrt(2) , θ = 315°)
another point is:
(r = 2 sqrt(2) , θ = 135°)

a million) Polar coordinates are given with 2 coordinates: the perspective of the line between the element to the beginning from the xaxis; and the dimensions of that line. although, you additionally can supply the complementary perspective, with a damaging sign. this is sparkling in case you seem at a graph that, because (5,5) bisects the fourth quadrant, the perspective is 40 5 stages. additionally, because of the fact the line is the hypotenuse, and a=b=5, we see that 25 + 25 = c*c = 50 = 25 * 2 . for this reason c = 5*Sqrt(2). So this is the two (7*40 5, c) or (40 5, c) 2) right here we would desire to apply arcsin or arccos. So this is ( variety(5*5 + pi/3 * pi/3) =c  arcsin ( pi/3 / c)

(2,2) is in the 4th quadrant,
so what's needed is a positive radius with theta=315 degrees
or a negative radius with theta=135 degrees.
Choice #3.