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], therefore
Frequency = [tex]\frac{1}{2}[/tex]
