Question

what is the equation of the sinusoid shown in the graph?
a. ( y = 4cos(\frac{1}{2}x) )
b. ( y=cos(\frac{pi}{2}x) )
c. ( y = 4cos(\frac{pi}{2}x) )
d. ( y = 4cos(2x) )

Explanation:

Step1: Identify amplitude

Amplitude = max y-value = 4.

Step2: Calculate period

From graph, period = distance between peaks = π (e.g., from 0 to π).

Step3: Find angular frequency

$\omega = \frac{2\pi}{\text{period}} = \frac{2\pi}{\pi} = 2$.

Step4: Form equation

Equation: $y = 4\cos(2x)$.

Answer:

D. $y = 4\cos(2x)$