Question

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

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 of the function.
For the solid - line cosine function:
The maximum value \(y_{max}=1\) and the minimum value \(y_{min}=-1\). The amplitude \(A=\frac{y_{max}-y_{min}}{2}=\frac{1 - (-1)}{2}=1\)

Step2: Find the period and \(B\)

The period \(T\) of a cosine function \(y = A\cos(Bx)+C\) is given by \(T=\frac{2\pi}{B}\).
For the solid - line cosine function, the period \(T = 2\pi\).
Using the formula \(T=\frac{2\pi}{B}\), and since \(T = 2\pi\), we have \(2\pi=\frac{2\pi}{B}\), so \(B = 1\)

Step3: Find the vertical shift \(C\)

The vertical shift \(C\) is the mid - line of the function. The mid - line is the average of the maximum and minimum values.
\(C=\frac{y_{max}+y_{min}}{2}=\frac{1+( - 1)}{2}=0\)

Answer:

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