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

Question

2867 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-25T16:47:28

$r=theta/2$

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 $r=theta/2$

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