How do you convert x=3 into a polar equation?

1 Answer
Apr 22, 2016

r=3 sec thetar=3secθ.

Explanation:

x=r cos thetax=rcosθ
So, x =3 becomes r cos theta = 3 or r = 3 sec thetarcosθ=3orr=3secθ

x = 3 is the straight line parallel to y-axis, in the first and fourth quadrants, at a distance 3 from the y-axis.

The polar forms of lines parallel to the axes are r = a sec theta, theta in (-pi/2, pi/2) and r = a csc theta, theta in (pi, 0)r=asecθ,θ(π2,π2)andr=acscθ,θ(π,0).
r ranges from +oo+ down to a and increase to +oo+.

Unless necessitated (in problems relating to radial directions), polar forms are avoided for equations of straight lines . .