Find an equation equivalent to r = 10 sin theta rectangular coordinates.

Question

asked Sep 11, 2021 117k views

2 Answers

Albert Alberto · Answer 1 · 2021-09-15T18:45:21+0000

We have been an equation in polar coordinates
$r=10\text{sin}(\theta)$ . We are asked to write our equation in rectangular coordinates.

We know that the equation
$r=2b\text{sin}(\theta)$ is equation of a circle with a radius
|b| and center at
(0,b) .

Let us find the value of b.

$2b\text{sin}(\theta)=10\text{sin}(\theta)$

$\frac{2b\text{sin}(\theta)}{2\text{sin}(\theta)}=\frac{10\text{sin}(\theta)}{2\text{sin}(\theta)}$

b=5

We know that equation of a circle in rectangular coordinates is
(x-h)^2+(y-k)^2=r^2

Since
b=5 , so radius is 5 and center is at point (0,5).

(x-0)^2+(y-5)^2=5^2

x^2+(y-5)^2=25

Therefore, our required equation would be
x^2+(y-5)^2=25 .