Question

How do you convert `r = 4/cos(theta)` into cartesian form?

Answer 1

`x=4`.

Explanation:

If `cos theta` is not 0, `r cos theta= x =4`.

The polar equation represents line parallel to y-axis ( `theta = 0` ),

at a distance 4, above..

If r is restricted to be `>=0` ( here,`>=4` ), the whole line is traceable, in polar mode, for `theta in (0, pi/2) and theta in ((3pi)/2, 2pi)`. There are infinite discontinuities for r at `theta = pi/2 and theta=(3pi)/2`..

Interestingly, the half-lines traced this way are made in the same

direction `theta = 0`.