The gradient of the function $y = \cos(x)$ at the point $x = 0$ is equal to $0$.

To understand this, we must first recall that the gradient (or slope) of a function at a specific point is determined by its derivative at that point. The derivative of the function $y = \cos(x)$ is given by

This derivative represents how the value of $\cos(x)$ changes as the variable $x$ varies.

Next, we need to evaluate this derivative at $x = 0$. By substituting $x = 0$ into the derivative $y' = -\sin(x)$, we find:

Since we know that $\sin(0) = 0$, it follows that

Thus, at $x = 0$, the gradient of the curve $y = \cos(x)$ is indeed $0$. This indicates that the slope of the tangent line to the curve at this point is flat, meaning there is neither an incline nor a decline.

This observation aligns with the graphical representation of $\cos(x)$, which reaches a peak at $x = 0$. At this peak, the curve changes direction, and the tangent line is horizontal, further confirming that the gradient at this point is $0$.