Question

State the amplitude and period of f(x) = 3cos9/5t

Answer 1

The amplitude is 3 and the period is 10π/9.

Explanation:

The standard cosine function is in the form:

`y=a\cos(b(x-c))+d`

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:

`f(x)=\displaystyle 3\cos(9)/(5)t`

We can rewrite this as:

`\displaystyle f(x)=(3)\cos\left((9)/(5)\left(t-0\right)\right)-(0)`

Therefore, a = 3, b = 9/5, c = 0, and d = 0.

Hence, our amplitude is |3| = 3.

Our period will be:

`\displaystyle \text{Period}=(2\pi)/(9/5)=2\pi \cdot (5)/(9)=(10\pi)/(9)`