Question

r Csc(θ) = -2 How do I convert from polar to rectangular coordinates with a Cosecant?

Answer 1

for a standard form of the equation,

To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) :

x = r × cos( θ )
y = r × sin( θ )

Answer 2

I may be looking at this the wrong way, but doesn't the Cosecant end up looking like r(1/sin(θ))=-2 ? This leads me to r/sin(θ)=-2. I'm not sure if this is the proper sequence of steps. Am I missing something?

Answer 3

I think I understand this now. this is the proper sequence. r/sin(θ)=-2, multiplying both sides by sin(θ) writes it in the standard form of r=-2sin(θ), which can then be multiplied by r on both sides, resulting in: r^2 = -2rSin(θ), which brings in the above posted rule of y = rsin(θ). I see now. Thanks