Thread: Polar and Rectangular coordinates

need help with these two problems:

1. For a give rectangle coordinate, find two pairs of polar coordinates for the poing. One pair satisfies r≥0 and 0≤theta<2pi, and the second pair satisies r≥0 and -2pi<theta≤0
for the problem (-3, 3sqrt(3))

2. Identify the curve by transforming Rsin(theta)=4 into rectangular coordinates.
So far, I converted it to 4csc(theta) but now i'm stuck.

Hello, stryker213!

1. For a given rectangle coordinates, find two pairs of polar coordinates for the point.
One pair satisfies r > 0 and 0 ≤ θ < 2π,
and the second pair satisfies r ≥ 0 and -2π < θ ≤ 0
for the problem (-3, 3√3)

We are given: .x = -3, .y = 3√3. .The point is in Quadrant 2.
. . . . . . . . . .____________
Then: .r .= .√(-3)² + (3√3)² .= .6

And: .tanθ .= .(3√3)/(-3) .= .-√3 . → . θ = 2π/3


The polar coordinates are: .(6, 2π/3) and (6, -4π/3)

2. Identify the curve by transforming r·sinθ = 4 into rectangular coordinates.

You're expected to know the conversion formulas: .x .= .r·cosθ, .y .= .r·sinθ

Then .r·sinθ = 4 .becomes .y = 4, a horizontal line.