Answer
$y= -\sin x$
Work Step by Step
Upon inspection, we find that the graph shows an inverted sin function with an amplitude of 1 and a period of $2\pi$.
The standard equation $y=a \sin bx$ becomes $y=-a \sin bx$ if the graph is an inverted sin function. In the equation $y=-a \sin bx$, $a$ is the amplitude. Since the amplitude is 1, $a$ is equal to 1. To find the value of $b$, we use the formula:
Step 1: Period$=\frac{2\pi}{b}$
Step 2: $2\pi=\frac{2\pi}{b}$
Step 3: $b=\frac{2\pi}{2\pi}$
Step 4: $b=1$
Substituting the values of $a$ and $b$ in the equation $y=-a \sin bx$, we find that the equation of the graph is $y= -\sin x$.
