Question

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

Answer 1

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:

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