Circadian rhythms are approximately 24hour internally controlled biological changes that occur in the absence of environmental cues although they can be altered by the environment. The first example that might pop in your mind when you hear circadian rhythms is the sleepwake cycle. Other examples include daily fluctuations in fluctuations in body temperature, hormones, behavior, and heart rate. Individual neurons in the suprachiasmatic nucleus, a cluster of cells in the region of the brain called the hypothalamus, generates this "biological clock" in mammals. But you don't need to have a brain to have a biological clock. Circadian rhythms are found in a wide variety of organisms from singlecelled yeast to plants.

Photo Credit: Julie Donoghue 
Mathematically, circadian rhythms can be modeled using trigonometric functions. There is not a general equation that encompasses all circadian rhythms. Instead, biologists and mathematicians must use empirical data to determine best model. For this module, we will consider a hypothetical example. Suppose a particular species exhibits daily regular fluctuations in body temperature that can be approximated by the equation,
where T represents temperature in°C, t represents time (in hours), and t = 0 corresponds to 12 o'clock midnight (i.e. 12:00 AM). 
Use the above equation to answer the following questions:
Problem 1 Find the body temperature at midnight.
Problem 2 Find the approximate body temperature at a given time.
Problem 3 Find the period of the function describing body temperature fluctuations.
Problem 4  What time of day does the body temperature reach a maximum.
Problem 5  What time of day does the body temperature reach a maximum.
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