Question

graph at least one full cycle of the of the following trig function label the amplitude midline minimum and the intervalsf(x)=1/3cps 2(x+pi)

Answer 1

Given the function

`f(x)=(1)/(3)\cos (2(x+\pi))`

Which is equivalent to

`\Leftrightarrow f(x)=(1)/(3)\cos (2x+2\pi))`

In general, a trigonometric equation has the following structure

`g(x)=A\cos (B(x-C))+D`

Where A is the amplitude.

Therefore, the amplitude of our function is 1/3.

As for the minimum and maximum of the function, remember that the range of the cosine function is [-1,1]; therefore,

`\begin{gathered} \text{minimum(f(x))}=(1)/(3)(-1)=-(1)/(3) \\ \text{maximum(f(x))}=(1)/(3)(1)=(1)/(3) \end{gathered}`

Furthermore, the midline of the graph is a parallel line to the x-axis that crosses the midpoint between the maximum and the minimum; in our case,

`\begin{gathered} ((1)/(3)+(-(1)/(3)))/(2)=0 \\ \Rightarrow\text{midline is y=0} \end{gathered}`

Finally, the graph of the function in the [0,2pi] interval is