A cosine function has an amplitude of 2 , a frequency of \( \frac{2}{\pi} \), and midline at \( y=3 \). What is an equation of this function? Move values to the lines to give an equation for this function. \( y=\quad 4 \pi \) \( 2 \pi \)

The equation of a cosine function can be expressed in the form \( y = A \cos(B(x - C)) + D \), where \( A \) is the amplitude, \( B \) is related to the frequency, \( C \) is the phase shift, and \( D \) is the midline. Given your values, the amplitude \( A = 2 \), the midline \( D = 3 \), and the frequency \( \frac{2}{\pi} \), we first find \( B \) as \( B = \text{Frequency} \times 2\pi = \frac{2}{\pi} \times 2\pi = 4 \). So we have: \[ y = 2 \cos(4(x - 0)) + 3 \] This simplifies to: \[ y = 2 \cos(4x) + 3 \] The resulting equation is \( y = 2 \cos(4x) + 3 \).