Question

graphing sine, cosine and tangent
ariel gaspar lopez
9 of 14
enter an equation that is represented by the graph.
$f(x)=3.5\cos \frac{3\pi}{2}$

Explanation:

Step1: Identify amplitude

The maximum value of the graph is 3.5, minimum is -3.5, so amplitude $A=3.5$.

Step2: Identify period

The graph completes one full cycle between $-\pi$ and $\pi$, so period $T=2\pi$. Use period formula $T=\frac{2\pi}{|B|}$ to solve for $B$:
$$2\pi=\frac{2\pi}{|B|} \implies |B|=1 \implies B=1$$

Step3: Check phase/vertical shift

The graph has a maximum at $x=0$, matching the basic cosine function (no phase shift, no vertical shift: $C=0, D=0$).

Answer:

$f(x)=3.5\cos(x)$