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 __
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)
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)