Question

A town's average monthly temperature data is represented in the table below: Average Monthly Month, x Temperature, °F January, 1 23.9 February, 2 28.0 March 3 38.4 April, 4 53.8 May, 5 70.9 83.2 July, 7 86.4 August, 8 $1.2 September, 9 812 October, 10 56.2 November, 11 40.6 December, 12 29.5 Ne, 6 Find a sinusoidal function of the form y = A sin (wx - ) + B that fits the data. y = 55.15 sin + 31.25 271 y = 31.25 sin - + 55.15 O y = 23.9 sin X- 5) + 86.4 y = 864 sin +23.9

Answer 1

Solution:

$\\y=A\sin(\omega x-\varphi )+B$

Where A is amplitude

$A=\frac{max-min}{2}$

max=86.4

min=23.9

$A=\frac{86.4-23.9}{2}=31.25$

y = 31.25 sin(Wr - 0 + B

From the option only one option is available.

$y=31.25\sin\left ( \frac{\pi}{6}x-\frac{2\pi}{3} \right )+55.15$

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