Question #67f1f

1 Answer
P dilip_k
Jul 15, 2017

Here the temperature varies in 24 hrs period from minimum value 60^@F60∘F to maximum value 80^@F80∘F. Hence its equilibrium value will be (60^@+80^@)/2=70^@F60∘+80∘2=70∘F

So the variation of temperature may be modeled by follwing a sinusoidal function of amplitude (80^@-70^@)=10^@F(80∘−70∘)=10∘F

f(x)=70+10sin((2pix)/24)=70+10sin((pix)/12)f(x)=70+10sin(2πx24)=70+10sin(πx12) in ""^@F∘F, where x is the time in hour.

The variation follows the following graph

enter image source here

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