Answer: Choice D
[tex](\sqrt{2}{, 45^{\circ})[/tex]
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Explanation:
The original point is in cartesian form (x,y). We have x = 1 and y = 1 pair up together.
The radius is [tex]r = \sqrt{x^2+y^2} = \sqrt{1^2+1^2} = \sqrt{2}[/tex]
The angle theta is [tex]\theta = \tan^{-1}(y/x) = \tan^{-1}(1/1) = 45^{\circ}[/tex]
Therefore, the polar form is [tex](r, \theta) = (\sqrt{2}, 45^{\circ})[/tex]
The idea is to start at the origin while facing directly east at the angle 0 degrees. Then turn 45 degrees to the north (going counterclockwise) and then move [tex]\sqrt{2}[/tex] units away from the origin. Doing these steps will take you to the point (x,y) = (1,1)
