Question

write the equation of the trigonometric function shown in the graph.

answer attempt 1 out of 2

Explanation:

Step1: Determine the amplitude

The general form of a cosine function is $y = A\cos(Bx)+C$. The amplitude $A$ is the distance from the mid - line to the maximum (or minimum) value. Looking at the graph, the maximum value is $1$ and the minimum is $- 1$. The mid - line is $y = 0$. So, $A=\frac{1 - (-1)}{2}=1$.

Step2: Determine the period

The period of the function $y=\cos(Bx)$ is $T=\frac{2\pi}{B}$. For the standard cosine function $y = \cos(x)$, the period is $2\pi$. Looking at the graph, the period of the given cosine - like function is $2\pi$. Using the formula $T=\frac{2\pi}{B}$, with $T = 2\pi$, we get $2\pi=\frac{2\pi}{B}$, so $B = 1$.

Step3: Determine the vertical shift

The vertical shift $C$ is the mid - line of the function. The mid - line of the given function is $y = 0$, so $C = 0$.

Answer:

$y = 1\cos(1x)+0$