Organisms are undoubtedly influenced by environment; certain environments are intolerable to certain species. Temperature, weather, the presence of competitors, and water availability are examples of abiotic and biotic environmental factors. Some examples include the emergence of insects such as cicadas, the acceleration of some amphibian life cycles when water resources diminish, seasonal reproduction, and the life cycle of many desert species.

Photo credit: NOAA Photo Library, NOAA Central Library; OAR/ERL/National Severe Storms Laboratory (NSSL)

This problem set will consider the hypothetical example of an experimentalist trying to determine how temperature affects the behavior of a newly discovered insect. In the laboratory, temperature is continuously varied, i.e. periodically forced, according to the trigonometric function,

where T represents temperature in °F and t represents time in hours (where t = 0 corresponds to the initiation of the experiment). Assume all other environmental factors remain roughly constant during the experiment.