# How do you find period, amplitude, and midline of f(t)=3cos(4t)+1?

Oct 13, 2017

$f \left(t\right) = 3 \cos \left(4 t + 0\right) + 1$
a Amplitude = 3
Period $= \frac{2 \pi}{b} = \frac{2 \pi}{3}$
Phase shift =(-c)/b=0
Vertical shift d = 1

#### Explanation:

Standard form $y = a \cdot \cos \left(b \left(\theta\right) + c\right) + d$
Where a is Amplitude and $\frac{2 \pi}{b}$ is period,
c/b is phase shift & d is vertical shift**

$f \left(t\right) = 3 \cos \left(4 t + 0\right) + 1$
a Amplitude = 3
Period $= \frac{2 \pi}{b} = \frac{2 \pi}{3}$
Phase shift =(-c)/b=0
Vertical shift d = 1