Question

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

Answer 1

`x^(2) + y^(2) - 10\cdot y = 0`

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`