Question

How do you graph `r=8sintheta`?

Answer 1

Graph is inserted. See explanation.

Explanation:

`r=2a cos(theta-alpha)`

represents the circle through the pole r = 0, with radius a and center

at `(a, alpha)`.

Here, a = 4 and `alpha = pi/2`'

For graphing here, convert to cartesian form using

`r(cos theta, sin theta ) = (x, y)` that gives,

`sin theta= y/r and r=sqrt(x^2+y^2)>=0.`

So, the cartesian form is

`sqrt(x^2+y^2)=8y/sqrt(x^2+y^2)` that gives the standard form

`x^2+(y-4)^2=4^2`

graph{x^2+y^2-6y=0 [-20, 20, -10, 10]}