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# Over a 24-hour period, the temperature in a town can be modeled by one period of a sinusoidal function.

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Over a 24-hour period, the temperature in a town can be modeled by one period of a sinusoidal function. The temperature measures 70°F in the morning, rises to a high of 80°F, falls to a low of 60°F, and then rises to 70°F by the next morning.

What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?

Jan 28, 2020

#1
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y = a·sin(b·x) + c

c is the value of the midline; c = 70

a is the amplitude (high or low from the midline); a = 10      (found by high - midline)

b is the modification of the period; 360° in a 24 hour day; b = 360/24.

Jan 28, 2020
#2
+1 This is correct in structure then, yes?

PeerlessCucumber  Jan 28, 2020
#3
+1

Thanks Gino,

What you need to do Peerless Cucumber  is  graph your formula with Desmos and see if it works.

Remember to use radians, not degrees.

(Note, Gino was using degrees but you changed it to radians)

Melody  Jan 29, 2020