Find the number of vertical tangents to the graph of the motion of a particle whose position vector is vector r with components, the 2 times the cosine of t, the sine of 2 times t . (10 points)
A) One
B) Two
C) Three
D) Four
2 answers
I cannot interpret your description.
x = 2cost
y = sin2t
dy/dx = (dy/dt) / (dx/dt) = (2 cos2t)/(-2sint) = -cos2t/sint
so vertical tangents occur when sint=0 and co2t≠0
t = kπ
Since x has period 2π, that's how long it takes to trace the curve, giving 2 vertical asymptotes.
y = sin2t
dy/dx = (dy/dt) / (dx/dt) = (2 cos2t)/(-2sint) = -cos2t/sint
so vertical tangents occur when sint=0 and co2t≠0
t = kπ
Since x has period 2π, that's how long it takes to trace the curve, giving 2 vertical asymptotes.