Question

at a certain location, the number of hours of sunlight is modeled by $y = 6.4cos(\frac{pi}{26}x)+12$, where $x$ represents the number of weeks after the summer solstice. based on the model, what is the minimum number of hours of sunlight at this location? 3.2 5.6 6.4 13.0

Explanation:

Step1: Recall cosine range

The range of the cosine function $y = \cos(t)$ is $[- 1,1]$.

Step2: Find minimum of given function

We have $y = 6.4\cos(\frac{\pi}{26}x)+12$. When $\cos(\frac{\pi}{26}x)=-1$, we get the minimum value of $y$.
Substitute $\cos(\frac{\pi}{26}x)=-1$ into the equation:
$y = 6.4\times(-1)+12$.
$y=-6.4 + 12$.
$y = 5.6$.

Answer:

B. 5.6