Questions: Question 12, 9.6.47 HW Score: 58.86%, 11.77 of 20 points Points: 0 of 1 Graph the following function y = 1/5 cos(1/4 x - π/16) Use the graphing tool to graph the function Click to enlarge graph (For any answer boxes shown with the grapher, type an exact answer Type the word pi to insert the symbol π as needed.)

Solution Steps

The given function is: \[ y = \frac{1}{5} \cos \left( \frac{1}{4}x - \frac{\pi}{16} \right) \]

The amplitude of the function is the coefficient of the cosine function: \[ \text{Amplitude} = \left| \frac{1}{5} \right| = \frac{1}{5} \]

The period of the cosine function is given by: \[ \text{Period} = \frac{2\pi}{\frac{1}{4}} = 8\pi \]

The phase shift is given by solving: \[ \frac{1}{4}x - \frac{\pi}{16} = 0 \] \[ x = \frac{\pi}{4} \]

1. Start by plotting the cosine function with the determined amplitude, period, and phase shift.
2. The function will have a maximum value of \(\frac{1}{5}\) and a minimum value of \(-\frac{1}{5}\).
3. The period is \(8\pi\), so the function will complete one cycle over this interval.
4. The phase shift is \(\frac{\pi}{4}\) to the right.

Final Answer