Given:
Amplitude of cosine function, A=3.
Period, T=7π/4.
Midline, D=2.
The time period can be expressed as:
[tex]T=\frac{2\pi}{B}[/tex]
Put T=7π/4 to find the value of B.
[tex]\begin{gathered} \frac{7\pi}{4}=\frac{2\pi}{B} \\ B=\frac{4\times2}{7} \\ =\frac{8}{7} \end{gathered}[/tex]
The general cosine function can be expressed as,
[tex]f(x)=A\cos (Bx)+D[/tex]
Substitute B=8/7, A=3 and D=2 in above equation.
[tex]f(x)=3\cos (\frac{8}{7}x)+2[/tex]
Therefore, the cosine function is,
[tex]f(x)=3\cos (\frac{8}{7}x)+2[/tex]
