To determine the properties of the constant \( c \), let's analyze the given sinusoidal function:
\[ F(t) = 8 \cos(72(t - c)) + 30 \]
The given function represents a sinusoidal function in the form \( A \cos(B(t - C)) + D \), where:
- \( A \) is the amplitude,
- \( B \) is the frequency (angular frequency),
- \( C \) is the phase shift, and
- \( D \) is the vertical shift (or midline).
Comparing the given function with the standard form, we can deduce the following about the constant \( c \):
1. The phase shift, \( C \), represents a horizontal shift of the graph. It determines where the function starts within its period.
2. The value of \( c \) will affect the position of the cosine function horizontally.
Since the given function represents temperatures in a town over time, \( c \) will indicate the time of the day when the temperature reaches its maximum or minimum value.
However, without additional information about the data or the context, we can't determine the specific value of \( c \) or make any definitive statements about it. We need to know more about the temperature data or the characteristics of the town's climate to determine the value of \( c \) accurately. Therefore, the correct answer is that without more context or information about the temperature data, we cannot determine the specific value of \( c \).
