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Irina-Kira [14]
3 years ago
10

Convert the equation r = 12 sin theta to Cartesian coordinates. Describe the resulting curve.

Mathematics
1 answer:
VLD [36.1K]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that there is a polar equation as

r=12 sin \theta

This has to be converted into cartesian.

We know the conversion is

r^2 =x^2+y^2 \\tan \theta = \frac{y}{x}

Using this we can say that

sin^2 \theta = 1-cos^2 \theta \\= 1-\frac{1}{sec^2 \theta} \\=1-\frac{1}{1+tan^2 \theta} \\=1-\frac{1}{1+\frac{y^2}{x^2} } \\=1-\frac{x^2}{x^2+y^2} \\=\frac{y^2}{y^2+y^2}

\sqrt{x^2+y^2} =12(\frac{y}{\sqrt{x^2+y^2} } \\x^2+y^2 =12y\\x^2+y^2-12y+36 = 36\\x^2+(y-6)^2 = 6^2}

Circle with centre (0,6) and radius 6.

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