1.) Which of the following polar equations is equivalent to the parametric equations below?

To convert the parametric equations x=t^2 and y=2t to polar form, we can use the equations x = r*cos(theta) and y = r*sin(theta).

From x = t^2, we have:
r*cos(theta) = t^2

From y = 2t, we have:
r*sin(theta) = 2t

Dividing the two equations gives:
tan(theta) = 2/t
tan(theta) = 2/(r*sin(theta))

Rearranging gives:
r*sin(theta)*tan(theta) = 2

Thus, the equivalent polar equation is:
r = 2/(sin(theta)*cos(theta))
r = 2/(1/2*sin(2*theta))
r = 2*csc(2*theta)

Therefore, the correct answer is:
C.) r = tan(theta)sec(theta)/4