The coordinates of a point on a circle of radius are given by

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The coordinates of a point on a circle of radius

a

are given by

x = a\cos t,\; y = a\sin t

. Determine

\dfrac{d^{2}y}{dx^{2}}

in terms of

t

and hence find its value when

t = \dfrac{\pi}{2}