Parameterization of the Circle

[vanitymdl]

Homework Statement

Consider the following parameterization of the circle:
a) x1 (t) = (cost, sint)

b) x2 (t) = (cos3t, sin3t)

c) x3 (t) = (sint, cost)

How long does it take point a particle to go from (1,0) to (0,1) for each parameterization.

Homework Equations

The Attempt at a Solution

(cos,sin) of (1,0) is 2pi then (cos, sin) of (0,1) is pi/2

how would I figure out the time it takes?

 

[SammyS]

Homework Statement

Consider the following parametrization of the circle:
a) x1 (t) = (cost, sint)

b) x2 (t) = (cos3t, sin3t)

c) x3 (t) = (sint, cost)

How long does it take point a particle to go from (1,0) to (0,1) for each parametrization.

Homework Equations

The Attempt at a Solution

(cos,sin) of (1,0) is 2pi then (cos, sin) of (0,1) is pi/2

how would I figure out the time it takes?

For each parametrization find a value of t for which x(t) = (1, 0), then find the next greater value of t for which x(t) = (0, 1) .

 

[DryRun]

Tricky wording.