Question

I need help with this practice problem solving This is trigonometry from my ACT prep guide

Answer 1

Take into account, that in general, a cosine function of amplitude A, period T and vertical translation b, can be written as follow:

$f(x)=A\cos (\frac{2\pi}{T}x)+b$

In the given case, you have:

A = 4

T = 3π/4

b = -3

By replacing you obtain:

$\begin{gathered} f(x)=4\cos (\frac{2\pi}{\frac{3\pi}{4}}x)-3 \\ f(x)=4\cos (\frac{8}{3}x)-3 \end{gathered}$

Hence, the answer is:

f(x) = 4cos(8/3 x) - 3