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The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.)

 

m0 1 2 3 4 5 6 7 8 9 10 11

f(m)62 50 41 38 41 50 62 74 83 86 83 74

 

A sine function is written to represent the data.

What is the amplitude, period, and vertical shift of this equation?

Drag a value into each box to correctly complete the statements.

 

The amplitude of the sine function is __. The period of the sine function is __. The vertical shift of the function is Response area __

 Mar 12, 2021

Best Answer 

 #1
avatar+31281 
+2

Highest   86     lowest   41        86-41 = 45     Amplitude is 1/2 of this = 22.5

22.5 sin

The graph starts at 62 and heads downward  so it is  - sin     (reflected)

shifted up     so midline is   (86+41)/2 = 63.5 up

 

- 22.5 sin (          )     + 63.5

Month zero = 62   so there is a very small shift of the graph to the left of .127

 -22.5 sin (  (x+.127)   )   + 63.5


 

Period is a year = 12 months       2pi / s  =  12      s =   pi/6

 

- 22.5 sin ( pi/6 (x+.127) + 63.5    =    temp                    where x = month          (this graph is not exact, but a 'best fit' for the data)  

 Mar 12, 2021
 #1
avatar+31281 
+2
Best Answer

Highest   86     lowest   41        86-41 = 45     Amplitude is 1/2 of this = 22.5

22.5 sin

The graph starts at 62 and heads downward  so it is  - sin     (reflected)

shifted up     so midline is   (86+41)/2 = 63.5 up

 

- 22.5 sin (          )     + 63.5

Month zero = 62   so there is a very small shift of the graph to the left of .127

 -22.5 sin (  (x+.127)   )   + 63.5


 

Period is a year = 12 months       2pi / s  =  12      s =   pi/6

 

- 22.5 sin ( pi/6 (x+.127) + 63.5    =    temp                    where x = month          (this graph is not exact, but a 'best fit' for the data)  

ElectricPavlov Mar 12, 2021

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