Ian

Seemingly straightforward question:

Convert (x,y) = (1,-1) to polar coordinates.

So, using x = rcosΘ and y = rsinΘ as the conversion equations, I go

1 = rcosΘ --> r = 1/cosΘ

Then

y = rsinΘ

-1 = sinΘ/cosΘ

--> Θ = 3π/4, 7π/4, which is what the answer key gives

However, when I plug in those Θ values to solve for r, I'm getting

r = 1/cosΘ

r = 1/cos(3π/4)

r = 1/(-SQRT(2)/2)

r = -2/SQRT(2)

So I have (7π/4, 2/SQRT(2)) and (3π/4, -2/SQRT(2))

instead of (7π/4, SQRT(2)) and (3π/4, -SQRT(2)), which is what the answer key gives.

Am I messing up a really easy problem, or is the answer key mistaken? Thanks!

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