What is the frequency of the function f(x)?f (x) = 3 cos (TX) – 2Express the answer in fraction form.

Accepted Solution

Answer:Frequency = [tex]\frac{1}{2}[/tex]Step-by-step explanation:We are given the following function and we are to find its frequency:[tex]f (x) = 3 cos (\pi x) -2[/tex]We know that the standard form of cosine function is [tex]y=Acos (Bx)+c[/tex]where [tex]A[/tex] is the amplitude, [tex]B=\frac{2\pi}{\text{Period}}[/tex] while [tex]c[/tex] is the mid line.Frequency is given by:[tex]F=\frac{1}{P}[/tex] where [tex]F[/tex] is frequency and [tex]P[/tex] is the period.Finding period by comparing the given function:[tex]y=3cos(\pi x)-2[/tex][tex]Period - B = \pi[/tex]Substituting B to get:[tex]\pi =\frac{2\pi}{\text{Period}}[/tex][tex]\text{Period}=\frac{2\pi}{\pi}=2[/tex]So, Period = 2.Since frequency is [tex]\frac{1}{P}[/tex], thereforeFrequency = [tex]\frac{1}{2}[/tex]