1. The problem asks which statement is true because the function $f(\theta) = \sin \theta$ is an odd function. 2. Recall the definition of an odd function: A function $f$ is odd if for all $\theta$, $f(-\theta) = -f(\theta)$. 3. Applying this to $\sin \theta$, we have the identity: $$\sin(-\theta) = -\sin(\theta)$$ which matches the definition of an odd function. 4. Let's analyze each statement: - Statement 1: "On the interval $[0, 2\pi]$, there are an odd number of points on the graph of $y = \sin \theta$ that fall on its midline." This is not necessarily true due to oddness. - Statement 2: "The maximum and minimum points of the graph of $y = \sin \theta$ occur at $\theta = \frac{k\pi}{2}$, where $k$ is an odd integer." This is true but not a direct consequence of oddness. - Statement 3: "The graph of $y = \sin \theta$ has reflective symmetry over the y-axis." This is false; odd functions have rotational symmetry about the origin, not reflective symmetry over the y-axis. - Statement 4: "For all values of $\theta$, $\sin(-\theta)$ is equal to $-\sin \theta$." This is exactly the definition of an odd function and is true. 5. Therefore, the true statement due to the oddness of $\sin \theta$ is: $$\sin(-\theta) = -\sin(\theta)$$ Final answer: For all values of $\theta$, $\sin(-\theta)$ is equal to $-\sin \theta$.