Question

Help me please i need this to be done for the assignment due tomorrow and i cant do it :(

conic section with polar equation:
r(theta)=(4/(3-sin(theta))

calculate the horizontal tangents and their concavity by calculating.

d2y/dx2=(d/dx)(dy/dx)=((d/d(theta)(dy/dx)/(dx/d(theta)))

Answer 1

x = rcos(theta) = (4*cos(theta))/(3 - sin(theta))
y = rsin(theta) = (4*sin(theta))/(3 - sin(theta))
then
dx = [(4*cos(theta))/(3 - sin(theta))]' * d(theta)
dy = [(4*sin(theta))/(3 - sin(theta))]' * d(theta)
so we can cal dy/dx
We determine horizontal tangents by let dy/dx = 0.
Hope this help.