Question

Convert the polar equation r = sin(θ) sec2(θ) to Cartesian coordinates and describe the resulting curve.

Answer 1

I assume you mean sec^2(θ) ?

I would change the sec to 1/cos
and multiply both sides to get r sin and r cos terms which are y and x in cartesian coords

Answer 2

*mult by r

Answer 3

can you try ?

Answer 4

obviuosly its the one @phi suggested

Answer 5

if it was not a square he was gonna put (2theta) and not 2(theta)

Answer 6

Here is one step you could take
\[ r = \sin(θ) \sec^2(θ) \]
\[ r= \frac{r}{r} \frac{\sin(\theta)}{\cos(\theta)} \frac{1}{\cos(\theta) } \]

you still have a cos to multiply by r, but if you multiply both sides by 1/r that will do it.

now use
x= r cos(A)
y= r sin(A)

to make it an equation in x and y