Thread: Show this curve has 2 tangents at (0,0)

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.

Originally Posted by CenturionMonkey

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.

no, (0,0) refers to x and y, not t. for instance, if t = 0, then x = 3, note zero. thus you would have the point (3,0), which is note what you want.

to find the slope of the tangent line, find where dy/dx = 0, and sove

Originally Posted by CenturionMonkey

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.

The cartesian point (0, 0) corresponds to and . Now note that the value of is different for these two values of .

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.