Problem 20 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find the period and amplitude. $$y=\frac{5}{2} \cos \frac{x}{4}$$

Step-by-Step Solution

Answer

The amplitude is \( \frac{5}{2}\) and the period is \(8\pi \).

Step 1: Determine the amplitude

The amplitude of a cosine function is the absolute value of the leading coefficient. In this case, the leading coefficient is \( \frac{5}{2}\), so the amplitude of \(y = \frac{5}{2} \cos \frac{x}{4}\) is \( \frac{5}{2}\).

Step 2: Determine the period

The period of a cosine function is calculated as \(2\pi\) divided by the absolute value of the coefficient of x inside the cosine function. In this case, the coefficient of x is \(\frac{1}{4}\), so the period is \(2\pi \times 4 = 8\pi \).