To determine the equation for the cosine function based on the given conditions, let's analyze the information provided:

1. Amplitude = 3: This means the coefficient in front of the cosine function is 3.

2. The function is "going down": This indicates that the cosine function should start with a negative amplitude, making it $-3$.

3. Period = $\frac{\pi}{2}$: For a cosine function, the period $T$ is determined by the formula: $T = \frac{2\pi}{B}$ where $B$ is the frequency modifier of the angle $\theta$ in $\cos(B \theta)$.

   Solving for $B$: $\frac{2\pi}{B} = \frac{\pi}{2}$ $B = 4$

Therefore, the equation that satisfies these conditions is: $y = -3 \cos(4\theta)$

The correct answer is: $y = -3 \cos 4\theta$

Would you like a further breakdown, or do you have any other questions?

Here are five related questions that build on this problem:

1. How would the equation change if the amplitude were increased to 5?
2. What would the equation look like if the function was a sine function instead?
3. How do we determine the phase shift of a trigonometric function?
4. What would the graph of this function look like?
5. How do amplitude and period affect the shape of a cosine wave?

Tip: Remember, the period of a cosine function is calculated by dividing $2\pi$ by the frequency modifier.