write the equation of the trigonometric graph. use a positive coefficient on cosine for this activity. y = □…

Explanation:

Step1: Find the amplitude

The amplitude $A$ is half the distance between the maximum and minimum values. The maximum value is $1$ and the minimum is $ - 1$, so $A=\frac{1 - (-1)}{2}=1$.

Step2: Find the period

The period $T$ is the horizontal distance between two consecutive peaks or troughs. From the graph, $T = 6$. The formula for the period of $y = A\cos(B(x - C))+D$ is $T=\frac{2\pi}{B}$. So, $6=\frac{2\pi}{B}$, and $B=\frac{\pi}{3}$.

Step3: Find the phase - shift

The graph is not shifted horizontally from the standard cosine graph (since it starts at a maximum at $x = 0$), so $C = 0$.

Step4: Find the vertical - shift

The mid - line of the graph is $y = 0$. The formula for the mid - line is $y=D$, so $D = 0$.

Answer:

$y = 1\cos\left(\frac{\pi}{3}(x - 0)\right)+0$ or simply $y=\cos\left(\frac{\pi}{3}x\right)$