Question

question
write the equation of the trigonometric function shown in the graph.
answer attempt 1 out of 2

Explanation:

Step1: Identify function type

The graph passes through the origin $(0,0)$, matches the shape of a sine function (no phase shift here), so we use the general form $y = A\sin(Bx)$, where $A$ is amplitude, $B$ relates to period.

Step2: Calculate amplitude $A$

Amplitude is half the distance between max and min $y$-values. The max $y$-value is 3, min is -3.
$A = \frac{3 - (-3)}{2} = 3$

Step3: Calculate period and $B$

The period $T$ is the length of one full cycle. From the graph, one cycle spans from $0$ to $2\pi$, so $T=2\pi$.
Using the period formula $T = \frac{2\pi}{|B|}$, substitute $T=2\pi$:
$2\pi = \frac{2\pi}{B}$
Solve for $B$: $B = \frac{2\pi}{2\pi} = 1$

Step4: Assemble the equation

Substitute $A=3$ and $B=1$ into $y = A\sin(Bx)$.

Answer:

$y = 3\sin(x)$