Replace the polar equations with equivalent Cartesian equations. Then describe or identify the graph. r=cot theta csc theta

miniliv4

miniliv4

Answered question

2022-09-30

Replace the polar equations with equivalent Cartesian equations. Then describe or identify the graph.
r = cot θ csc θ

Answer & Explanation

seppegettde

seppegettde

Beginner2022-10-01Added 7 answers

Since cot θ = cos θ / sin θ and csc θ = 1 / sin θ ,multiply sin 2 θ to both sides of the equation and obtain r sin 2 θ = cos θ . Multiply r to both sides of the equation again, we obtain r 2 sin 2 θ = r cos θ . Since x = r cos θ and y = r sin θ , so the Cartesian equation y 2 = x, which is a side-way parabola with vertex at the origin opening to the right.
Polar coordinates and Cartesian coordinates conversion:
r = x 2 + y 2
θ = tan 1 ( y x )
x = r cos θ
y = r sin θ
Result:
x = y 2

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