Question

What is an equation for a spiral of Archimedes that passes through `A(pi/4, pi/2)`?

Answer 1

`r=theta/2`

Explanation:

The polar equation of Archimedes' spiral is of the form

`r=atheta`, where `a` is a constant.

As this passes through `A(pi/4,pi/2)`, we have

`pi/4=axxpi/2`

i.e. `a=pi/4xx2/pi=1/2`

and equation of Archimedes' spiral is `r=theta/2`