Consider a circle of radius 2 and a pointProtating around it

Consider a circle of radius 2 and a pointProtating around it, as shown in the figure to the left, below.

Solution

theta(t) is a parabolic function with roots of 0 and 4 and a vertex at (2, 12) Therefore, the function can be represented as: T(t) = a(t-0)(t-4) T(t) = a(t)(t-4) use (2,12) to find the value of a 12 = a(2)(-2) 12 = -4a a = -3 T(t) = -3(t)(t-4) therefore, theta at t = 2.5 would be: T(2.5) = -3(2.5)(2.5-4) T(2.5) = -7.5(-1.5) T(2.5) = 11.25 radians Since the point P is going around the circle of radius 2 centered at the origin, the equation is modeled as: x^2 + y^2 = r^2 x^2 + y^2 = 4 x = rcos(theta) y = rsin(theta) therefore at t = 2.5 the point P is located at: x = 2cos(11.25) = 0.503379 y = 2sin(11.25) = -1.935616 voila and BOL