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Can anyone help with this trig function problem?  I'm not getting it.

 

g is a trigonometric function of the form g(x)=a*cos(bx+c)+d Below is the graph of g(x). the function has a maximum point at (, -2) and a minimum point at (, -14). Find a formula for g(x), . Give an exact expression.

 

 Jul 17, 2020
 #1
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The usual amplitude of a sin or cos wave is  1     and they go from +1 to -1   ( a height of 2   amplitude = height/2)

   this wave goes from -14 to -2   a height of 12      height/2 = 6 for amplitude

 

so 'a' in your equation is 6   it multiplies the wave by 6

6 cos (bx+c ) + d

'd' shifts the wave up or down.... the usual sin or cos wave has a midline at  y = 0

   ths one has a midline at y = -8    shifted down 8

 

6 cos (bx+c) - 8

'b' stretches or compresses the wave

     usual period for sin or cos wave is 2pi

        this one has 1/2 of a period from  3/4 pi to 2 pi     full period is   2* (2pi- 3/4 pi ) = 10/4 pi

           it is stretched out by 'b'       2pi / ( 10/4 pi) = 8/10 = 4/5 =b

6 cos (4/5 x +c) -8    

      'c'  shifts the wave left or right ...

           this cos wave is shited RIGHT  3/4 pi     (the high point of cos wave is usually at 0 this one is at 3/4 pi)

                SUBTRACTING SHIFTS RIGHT

                     BUT wecompressed the wave with 'b'  so 'c' will need to be compressed too

                           3/4 pi  * 4/5 = 3/5 pi

 

6 cos (4/5 x -3/5 pi ) - 8  

 Jul 17, 2020

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