1. **State the problem:** Simplify or understand the function $-\cos(x)$. 2. **Recall the cosine function:** The cosine function $\cos(x)$ gives the horizontal coordinate of a point on the unit circle at an angle $x$. It ranges from $-1$ to $1$. 3. **Apply the negative sign:** The function $-\cos(x)$ simply reflects the cosine graph across the x-axis. This means every value of $\cos(x)$ is multiplied by $-1$. 4. **Properties:** - The range of $-\cos(x)$ is also $[-1,1]$. - The function $-\cos(x)$ has the same period as $\cos(x)$, which is $2\pi$. - The zeros of $-\cos(x)$ are the same as those of $\cos(x)$, occurring at $x=\frac{\pi}{2} + k\pi$ for integers $k$. 5. **Final expression:** The function is $y = -\cos(x)$, which is the cosine wave flipped vertically. This completes the explanation and understanding of the function $-\cos(x)$.