Hey, this is my final question for my assignment. Needless to say, i'm stuck.
Use the given curve to answer the following questions.
x = 3cos(t)
y = sin(t)cos(t)
(a)Show that this curve has two tangents at (0, 0) and find their equations.
y=? (smaller slope)
y=? (larger slope)
i did this:
dy/dx = (dy/dt)/(dx/dt) = ((cost)^2 - (sint)^2)/-3sint
so since i know it's at (0,0), i know that i have to sub t=0, but if i do that then the slope becomes undefined. so i dont know what i'm doing wrong here. I appreciate any help, thanks.
ps. i want to thank everyone for helping me tonight with my assignment, and sorry for not writing it in that fancy math code, i dont know how to do trig that way.
I haven't looked closely but it's likely that (0, 0) is a double point, that is, a point at which the curve intersects itself. A double point is an example of a crunode.