# Second Derivative of Parametric Equation

Calculus Level 3

Let $x,y : \mathbb{R} \to \mathbb{R}$ be functions satisfying $y(t) = \sin^2 t$ and $x(t) = \cos t$ for all $t$. The second derivative $\frac{d^2 y}{d x^2}$ is a constant function, equal to $a$ everywhere. Find the value of $a$.

×