# Parameterization of the Circle

## 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.

## 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?

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SammyS
Staff Emeritus
Homework Helper
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## 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.

## 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
Gold Member
Tricky wording. 