The position vector of a particle moving in the x-y plane is vector components 2 times the cosine of t, 4 times the sine of t in the interval [0, 2π). For what value(s) of t does the path...

Question

The position vector of a particle moving in the x-y plane is  in the interval [0, 2π). For what value(s) of t does the path of the particle have a horizontal tangent?

A	0, π
B
C
D	None of these

Answer 1

r(t) = <2cost,4sint>; v(t) = r'(t) = <- 2sint, 4cost>.

Horizontal tangent line when dy/dx = 0; dy/dx = (dy/dt)/(dy/dx) = 4cost/(-2sit) = - 2cott = 0;

cott = 0; t =π/2 or t = 3π/2.

Ansewr is B