Question

ILL GIVE POINTS!! PLS HELP !!!

Which set of polar coordinates describes the same location as the
rectangular coordinates (1. - 1)?
A. (sqrt2,315°)
B. (-1,135°) C. (sqrt2,225°)
D. (1,45°)

Answer 1

The polar coordinates appear in the form (r, θ), where r is the the radius from the center and θ is the angle. To get the radius, do the following.

`r = √(x^2 + y^2) = √(1^2 + (-1)^2) = √(2)\\`

You can get the angle visually by drawing a point (1, -1) on a graph and seeing that it is 45 degrees from the top right quadrant (you can tell its 45 because both x and y have the same magnitude). Since there are 360 degrees, 360 - 45 = 315.

If you would like to find it mathematically, this is the way to do it

`\theta = atan(y/x) = -45`

Notice that -45 degrees is just 360 - 45 = 315

Your answer would be

`(√(2), 315)`