Get the solution to "Transform polar function r=−4sin⁡(θ) to rectangular coordinates and..."

High School
Calculus and Analysis
Calculus 2
Parametric equations

Efan Halliday

Answered question

2021-09-09

Transform polar function

r = - 4 \sin (θ)

to rectangular coordinates and graph, label your your graph clear with axes and scales

Answer & Explanation

irwchh

Skilled2021-09-10Added 102 answers

$r = - 4 \sin θ$
$=> r^{2} = - 4 r \sin θ (M u l t i p l i e d b o t h s i d e s b y r)$
$\Rightarrow x^{2} + y^{2} = - 4 y (∵ r^{2} = x^{2} + y^{2}, x = r \cos θ, x = r \cos θ and y = r \sin θ)$
$\Rightarrow x^{2} + y^{2} + 4 y = 0$
$\Rightarrow x^{2} + y^{2} + 4 y + 4 - 4 = 0$
$\Rightarrow x^{2} + {(y + 2)}^{2} = 4$
$\Rightarrow {(x - 0)}^{2} + {(y - (- 2))}^{2} = {(2)}^{2}$

Equation of a circle with radius $R = 2$ and center $(0, - 2) = C$

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