Question

How do you find the points of intersection of `r=4-5sintheta, r=3sintheta`?

Answer 1

`(r,theta)in{(3/2,pi/6+2kpi),(3/2,(5pi)/6+kpi)}, kinZZ`

Explanation:

If
`color(white)("XXX")r=4-5sin(theta)`
`color(white)("XXX")r=3sin(theta)`
then
`color(white)("XXX")3sin(theta)=4-5sin(theta)`

`color(white)("XXX")8sin(theta)=4`

`color(white)("XXX")sin(theta)=1/2`

For `theta in [0,2pi)`
`color(white)("XXX")theta=pi/6color(white)("xxxxxxx")orcolor(white)("xx")theta=(5pi)/6`
or to be complete
`color(white)("XXX")theta=pi/6+2kpicolor(white)("xx")orcolor(white)("xx")theta=(5pi)/6+2kpicolor(white)("XXX")kinZZ`

and since `r=3sin(theta)`
`color(white)("XXX")r=3*1/2 = 3/2`