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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?

Respuesta :

Answer:

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

Step-by-step explanation:

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

At time t (seconds),

[tex]x(t) = 10 sin(200t + 3) + 30[/tex]

and

[tex]y(t) = 10 cos(200t + 3) + 40[/tex]

[tex]x-30 = 10 sin(200t + 3) \\y-40 = 10 cos(200t + 3) + 40[/tex]

when we square and add both the equations we get

[tex](x-30)^2 + (y-40)^2 = 1[/tex]

(since sin square + cos square = 1 always)

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

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