Question

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

Answer 1

Answer:

x^2+y^2=10y

Step-by-step explanation:

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Answer 2

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