Find the midline of the function y=(6cos(6t)-7)/(2) ?

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Answer 1 · 2018-08-06T12:57:22

#y = - 3.5#

The vertical shift d of

#y = a cos ( bt + c ) + d#

gives the midline equation #y = d#.

Here,

#y = 3 cos ( 6 t ) - 3.5#. So, the axis ( midline ) of this cosine wave is

#y = - 3.5.

The period = #(2pi)/6 = pi/3# and the amplitude = 3.

See graph that reveals this axis.
graph{(y - 3cos ( 6x ) + 3.5)(y+3.5 + 0x)(y+6.5 +0x)(y+0.5+0x)=0[-2 2 -7 0]}

The graph is not on uniform scale, to favor better visual effect.