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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.)

A sine function is written to represent the data.

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

The amplitude of the sine function is ________. The period of the sine function is ______. The vertical shift of the function is _______.

 Mar 8, 2024

Best Answer 

 #1
avatar+394 
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A period is the distance between each repetition.
It's easy to see that after 12, f(m) starts repeating again.

Therefore the period is 12.

The vertical shift of this function is how much it's shifted up.

The sine function started at 50, so the vertical shift is 50 (also it's easy to see 50 is the midpoint).

Because 3 is right in between 0 and 6, it is the max value, similarly 9 is the min value.

So 50-33 = 17, and 67-50 = 17 too, so the amplitude is 17.

Therefore, The amplitude of the sine function is 17. The period of the sine function is 12. The vertical shift of the function is 50.

If it interests you, the equation of the function is \(f(m)=-17\sin(\frac{2\pi}{12}m)+50\).

 Mar 9, 2024
 #1
avatar+394 
+4
Best Answer

A period is the distance between each repetition.
It's easy to see that after 12, f(m) starts repeating again.

Therefore the period is 12.

The vertical shift of this function is how much it's shifted up.

The sine function started at 50, so the vertical shift is 50 (also it's easy to see 50 is the midpoint).

Because 3 is right in between 0 and 6, it is the max value, similarly 9 is the min value.

So 50-33 = 17, and 67-50 = 17 too, so the amplitude is 17.

Therefore, The amplitude of the sine function is 17. The period of the sine function is 12. The vertical shift of the function is 50.

If it interests you, the equation of the function is \(f(m)=-17\sin(\frac{2\pi}{12}m)+50\).

hairyberry Mar 9, 2024

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