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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.

Write the equation of the following sinusoid in terms of the cosine function.

Learn how to derive the equation of a sinusoidal function based on amplitude, vertical shift, period, and phase shift. This detailed guide helps students in high school understand key concepts in trigonometry and sinusoidal functions.

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