Question

PLEASE HELP!!! 15 PTS!!

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Convert the rectangular coordinates (√2, -√2) into polar coordinates. Express all angles in degrees rounded to the nearest degree.

A. (2, 180°)
B. (2, 0°)
C. (2, -45°)
D. (2, 45°)

Answer 1

`\large\boxed{C.\ (2,\ -45^o)}`

Explanation:

Regular coordinates (x, y)

Polar coordinates (r, φ)

`r=√(x^2+y^2)\\\\\psi=\arctan(y)/(x)`

We have the point

`(\sqrt2,\ -\sqrt2)`

Substitute:

`r=√((\sqrt2)^2+(-\sqrt2)^2)=√(2+2)=\sqrt4=2\\\\\psi=\arctan\left((-\sqrt2)/(\sqrt2)\right)=\arctan(-1)=-45^o`