To solve this, let's analyze the sinusoidal graph in terms of the cosine function. Here are the key parameters from the graph:

1. Amplitude: The maximum and minimum values of the sinusoid are 8 and 2, respectively. The amplitude $A$ is the distance from the midline to the peak, which is: $A = \frac{8 - 2}{2} = 3$

2. Vertical shift: The midline is halfway between the maximum and minimum values, so the vertical shift $D$ is: $D = \frac{8 + 2}{2} = 5$

3. Period: The graph completes one full cycle from $-360^\circ$ to $360^\circ$, so the period $T$ is: $T = 360^\circ - (-360^\circ) = 720^\circ$ The period of a cosine function is given by $T = \frac{360^\circ}{B}$, so solving for $B$: $B = \frac{360^\circ}{720^\circ} = \frac{1}{2}$

4. Phase shift: From the graph, the function appears to be shifted to the right by $90^\circ$. Since the cosine function starts at its maximum value, this is a phase shift of $90^\circ$ to the right. The phase shift is represented as $C = -90^\circ$.

Thus, the equation of the sinusoidal function in terms of cosine is: $y = 3 \cos\left(\frac{1}{2}(\theta + 90^\circ)\right) + 5$

Would you like further details on how to derive any specific part of this equation?

5 Related Questions:

1. How do you convert a sine function into a cosine function?
2. What effect does the phase shift have on the graph of a cosine function?
3. How do you calculate the period of a trigonometric function?
4. What is the relationship between amplitude and vertical stretching?
5. How would the graph change if the period were halved?

Tip: Always pay attention to the vertical shift when dealing with sinusoidal graphs. It helps you identify the midline, which is essential for writing the correct equation.