Question

Find the amplitude and period of the function. Y = 3/4 cos 4xGive the exact values, not decimal approximations.

Answer 1

Given the function:

$y=\frac{3}{4}\cos (4x)$

If we compare this to the general form:

$y=A\cos (bx+\delta)$

Where A is the amplitude, δ is the phase and b is a parameter, we identify:

$\begin{gathered} A=\frac{3}{4} \\ \delta=0 \\ b=4 \end{gathered}$

So the amplitude of the function is 3/4.

For the period, we need to remember that the period of a cosine function is 2π. Then:

$y=\frac{3}{4}\cos (4x)=\frac{3}{4}\cos (4x+2\pi)=\frac{3}{4}\cos (4(x+\frac{\pi}{2}))$

So the period of the function is π/2.