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A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is 7pi/12. The graph of the function does not show a phase shift. What is the equation of the cosine function described?

 

Fill in the blanks using values from this list: -20, -11, -9, -2, 2, 9, 11, 20, 7pi/12,12pi/7,7/24,24/7

 

 

f(x)=___cos(_____x)______

 May 28, 2020
 #1
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With no phase shift, the equation is:  y  =  a·cos(b·x) + d

 

since this is to be a reflection of its parent function over the x-axis, a must be negative

and a is the amplitude:    a  =  -11

 

b reflects the period:  b  =  2·pi/period   --->   b  =  2·pi/(7·pi/12)  =  24/7

 

d represents the vertical  d  =  -9

 

equation:  y  =  -11·cos( (24/7)·x ) - 9

 May 28, 2020

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