Question

Write a cosine function that Has a midline of 2 an amplitude of 3 and a period of 7pi/4

Answer 1

Given:

Amplitude of cosine function, A=3.

Period, T=7π/4.

Midline, D=2.

The time period can be expressed as:

$T=\frac{2\pi}{B}$

Put T=7π/4 to find the value of B.

$\begin{gathered} \frac{7\pi}{4}=\frac{2\pi}{B} \\ B=\frac{4\times2}{7} \\ =\frac{8}{7} \end{gathered}$

The general cosine function can be expressed as,

$f(x)=A\cos (Bx)+D$

Substitute B=8/7, A=3 and D=2 in above equation.

$f(x)=3\cos (\frac{8}{7}x)+2$

Therefore, the cosine function is,

$f(x)=3\cos (\frac{8}{7}x)+2$