Question

Car is moving on a circle on a plane. At time t (seconds), its x-coordinate is given by x(t) = 10 sin(200t + 3) + 30 while its y-coordinate is given by y(t) = 10 cos(200t + 3) + 40. what is the center and radius?

Answer 1

we have centre of circle as (30,40) and radius = 1

Explanation:

Given that a car is moving on a circle on a plane.

At time t (seconds),

`x(t) = 10 sin(200t + 3) + 30`

and

`y(t) = 10 cos(200t + 3) + 40`

`x-30 = 10 sin(200t + 3) \\y-40 = 10 cos(200t + 3) + 40`

when we square and add both the equations we get

`(x-30)^2 + (y-40)^2 = 1`

(since sin square + cos square = 1 always)

i.e. we have centre of circle as (30,40) and radius = 1