The image shows a sine wave graph with marked points $P$, $Q$, $R$, and $S$. The task is to determine the coordinates of these points based on their locations on the sine wave.

From the graph:

• The sine wave seems to have an amplitude of 2, meaning its maximum height is 2 and minimum height is -2.
• The sine wave starts at the origin and completes one full cycle by $x = \pi$.

Coordinates of Points:

1. Point $P$ is at the origin of the sine wave. It is the starting point: $P(0, 0)$
2. Point $Q$ is at the peak of the sine wave, where $y = 2$. It seems to occur at $x = \frac{\pi}{2}$: $Q\left(\frac{\pi}{2}, 2\right)$
3. Point $R$ is at the next zero crossing after the peak, which happens at $x = \pi$, where $y = 0$: $R(\pi, 0)$
4. Point $S$ is at the lowest point of the sine wave, where $y = -2$. It appears to occur at $x = \frac{3\pi}{2}$: $S\left(\frac{3\pi}{2}, -2\right)$

These coordinates are based on a standard sine function with an amplitude of 2.

Would you like more details on how sine functions behave? Here are some questions to consider:

1. How does the period of a sine function affect the spacing of points on the graph?
2. What is the relationship between amplitude and the y-coordinates of peak points?
3. How can you find the coordinates of other points on a sine wave?
4. How would the coordinates change if the sine wave had a phase shift?
5. What would the coordinates be if the amplitude were different?

Tip: When working with trigonometric graphs, understanding the function's amplitude, period, and phase shift is key to determining key points like peaks, zero crossings, and troughs.