Step 1: Understanding Inverse Functions and Their Graphs

The graph of the inverse of a function $f(x)$ is obtained by reflecting the graph of $f(x)$ about the line $y = x$. This means that if a point $(a, b)$ lies on the graph of $f(x)$, then the point $(b, a)$ lies on the graph of its inverse.

Step 2: Visualizing the Reflection

Imagine the given trigonometric function's graph being reflected across the line $y = x$. The x-axis becomes the y-axis and vice versa. The general shape of the graph will change accordingly.

Step 3: Analyzing the Options (Without Visuals)

Without the actual graphs (A, B, C, D), it's impossible to definitively choose the correct one. However, we can infer some characteristics the inverse graph should have:

- If the original function has a range of $[a, b]$, the inverse will have a domain of $[a, b]$.

- If the original function has a domain restriction to be invertible, the inverse will reflect that in its range.

Since we don't have the graphs, we cannot proceed further.