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Answer 1 · 2016-02-24T00:32:32

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

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#