Answer:
The amplitude is 3 and the period is 10π/9.
Step-by-step explanation:
The standard cosine function is in the form:
[tex]y=a\cos(b(x-c))+d[/tex]
Where |a| is the amplitude, 2π/b is the period, c is the phase shift, and d is the vertical shift.
We have the function:
[tex]f(x)=\displaystyle 3\cos\frac{9}{5}t[/tex]
We can rewrite this as:
[tex]\displaystyle f(x)=(3)\cos\left(\frac{9}{5}\left(t-0\right)\right)-(0)[/tex]
Therefore, a = 3, b = 9/5, c = 0, and d = 0.
Hence, our amplitude is |3| = 3.
Our period will be:
[tex]\displaystyle \text{Period}=\frac{2\pi}{9/5}=2\pi \cdot \frac{5}{9}=\frac{10\pi}{9}[/tex]
