Question #9aee7

1 Answer
Feb 24, 2016

f(t)=2sin(pi*t+pi)+1

Explanation:

This kind of wave has the general equation
f(t)=Asin(omega*t+t_0)+k
where

A=amplitude
omega=2pi*f=(2pi)/T
t_0 is the phase change or phase shift of the sinoidal wave
k is the vertical dislocation

Amplitude (("maximum"-"minimum")/2)

A=(3-(-1))/2=4/2=2

Period (T), horizontal distance between peaks, or the smallest distance where the function repeats itself

T=2-0=2
So
omega=(2pi)/T=(cancel(2)pi)/cancel(2) => omega=pi

t_0
The function sine is shifted half cycle forward (or backward), in radians, since a full cycle corresponds to 2pi, then t_0=pi

k
The axis of the function is one unit above the reference axis
So k=1
It can also be found by the mean:

-> k= ("maximum"+"minimum")/2=(3+(-1))/2=1

Using the results in the general formula:

f(t)=2*sin(pi*t+pi)+1