To analyze how the graph changed when the function went from $y = \sin \theta$ to $y = 5 \sin \theta$, let's break down the transformations:

1. Original Function: $y = \sin \theta$

   • Amplitude: 1 (since the coefficient of $\sin \theta$ is 1)
   • Period: $2\pi$ (standard period for the sine function)
   • Phase Shift: None
   • Vertical Shift: None

2. New Function: $y = 5 \sin \theta$

   • Amplitude: The coefficient of $\sin \theta$ is now 5, which means the amplitude has changed from 1 to 5.
   • Period: Remains $2\pi$ (since there's no change in the argument of $\theta$; it’s not multiplied or divided by any value affecting the period).
   • Phase Shift: None (no horizontal shift is indicated).
   • Vertical Shift: None.

Based on these observations, the correct answer is:

• The amplitude changed from 1 to 5.

This is the only transformation in this scenario, as the period, phase shift, and vertical shift remain unaffected.

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:

1. How does changing the amplitude affect the maximum and minimum values of the sine function?
2. What would happen to the period if the function were $y = \sin(5\theta)$ instead of $y = 5 \sin \theta$?
3. How does a phase shift affect the graph of a sine function?
4. What is the difference between a phase shift and a vertical shift in trigonometric functions?
5. How would the graph change if we added a constant, like $y = 5 \sin \theta + 3$?

Tip: When analyzing transformations of trigonometric functions, focus on changes to the amplitude, period, phase shift, and vertical shift separately for clarity.