To identify the equation of the graph in the image, we will analyze its key characteristics.

Observations:

1. Amplitude: The graph oscillates between $y = 1$ and $y = -1$, meaning the amplitude is $1$.
2. Period: The graph completes one full cycle from $x = 0$ to $x = 180^\circ$. The period is $180^\circ$.

Equation of a Sine Function:

The general equation for a sine function is: $y = \sin(kx)$ where:

• $k = \frac{360^\circ}{\text{Period}}$.

Here: $k = \frac{360^\circ}{180^\circ} = 2.$

Thus, the equation is: $y = \sin(2x).$

Correct Answer:

The correct option is (c) $y = \sin 2x$.

Would you like further clarification or additional examples?
Here are 5 related questions to explore:

1. How does the period of a sine wave change with $k$?
2. How is the amplitude reflected in the sine function equation?
3. What would the equation be if the period was $90^\circ$?
4. How can the phase shift of a sine graph be determined?
5. What are the key differences between sine and cosine graphs?

Tip: Always check the period of the graph to determine $k$ when identifying trigonometric equations!