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Vaselesa [24]
3 years ago
6

Find an equation equivalent to r = 10 sinθ in rectangular coordinates

Mathematics
1 answer:
Flura [38]3 years ago
8 0

Answer:

x^{2} + y^{2} - 10\cdot y = 0

Step-by-step explanation:

The following expressions are used to transform from polar into rectangular form:

r = \sqrt{x^{2}+y^{2}}

\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}

Now, the variables are substituted and equation is finally simplified:

\sqrt{x^{2}+y^{2}} = 10\cdot \frac{y}{\sqrt{x^{2}+y^{2}} }

x^{2}+y^{2} = 10\cdot y

The equivalent equation in rectangular coordinates is:

x^{2} + y^{2} - 10\cdot y = 0

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