Question

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

Explanation:

Step1: Find 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 given sine - wave is \(y = 1\) and the minimum value is \(y=-1\). So, \(A=\frac{1 - (-1)}{2}=1\).

Step2: Find the period and \(B\)

The general formula for the period \(T\) of a sine function \(y = A\sin(Bx)+C\) is \(T=\frac{2\pi}{B}\). The period of the given sine - wave is \(T = 2\pi\). Using the formula \(T=\frac{2\pi}{B}\), and substituting \(T = 2\pi\), we get \(2\pi=\frac{2\pi}{B}\), which implies \(B = 1\).

Step3: Find the vertical shift \(C\)

The vertical shift \(C\) of a sine function \(y=A\sin(Bx)+C\) is the mid - line of the function. The mid - line is \(y = 0\) (since \(\frac{1+( - 1)}{2}=0\)).

Answer:

\(y = 1\sin(1x)+0\)