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Amiraneli [1.4K]
3 years ago
7

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

Mathematics
2 answers:
Aleksandr [31]3 years ago
7 0

Answer:

x^2+y^2=10y

Step-by-step explanation:

d on edg

bazaltina [42]3 years ago
4 0

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.

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