write the equation of the trigonometric graph. y = sin ( x ) + answer attempt 1 out of 2 you must answer all…

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a sine - function $y = A\sin(Bx)+C$ is half the distance between the maximum and minimum values. The maximum value of the graph is $y = 1$ and the minimum value is $y=- 1$. So, $A=\frac{1 - (-1)}{2}=1$.

Step2: Determine the period and find $B$

The period $T$ of a sine - function $y = A\sin(Bx)+C$ is given by $T=\frac{2\pi}{B}$. The graph repeats itself every $2\pi$ units, so $T = 2\pi$. Since $T=\frac{2\pi}{B}$ and $T = 2\pi$, then $B = 1$.

Step3: Determine the vertical shift

The mid - line of the graph is $y = 0$. For the function $y=A\sin(Bx)+C$, the vertical shift is $C$. Since the mid - line is $y = 0$, then $C = 0$.

Answer:

$y = 1\sin(1x)+0$ or simply $y=\sin(x)$