Question

Find amplitude, midline, phase shift and period of the following equation.

Answer 1

The general cosine equation is:

`y=a\cdot cos\lbrack b(x-h)\rbrack+k_{}`

where,

`\begin{gathered} amplitude=|a| \\ period=(2\pi)/(b) \\ phase-shift=h \\ y=k\text{ is the midline} \end{gathered}`

In this case,

`y=3\cdot\cos \lbrack(1)/(2)(x-\pi)\rbrack+5`

where:

`\begin{gathered} a=3 \\ b=(1)/(2) \\ h=\pi \\ k=5 \end{gathered}`

Then,

`\begin{gathered} |3|=3\text{ is the amplitude} \\ (2\pi)/((1)/(2))=2\pi\cdot2=4\pi\text{ is the period } \\ \pi\text{ is the phase shift} \\ y=5\text{ is the midline} \end{gathered}`