Question

write the equation of the trigonometric function shown in the graph.
answer
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Explanation:

Step1: Find the amplitude

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

Step2: Find the period

The period \(T\) of a cosine function \(y = A\cos(Bx)+C\) is given by \(T=\frac{2\pi}{B}\). From the graph, the period \(T = 2\pi\). Using the formula \(T=\frac{2\pi}{B}\), substituting \(T = 2\pi\) gives \(2\pi=\frac{2\pi}{B}\), so \(B = 1\).

Step3: Find the vertical shift

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

Answer:

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