Questions: The normal monthly high temperatures H (in degrees Fahrenheit) in Erie, Pennsylvania, are approximated by H(t) = 57.54 - 18.53 cos(πt/6) - 14.03 sin(πt/6) and the normal monthly low temperatures L are approximated by L(t) = 42.03 - 15.99 cos(πt/6) - 14.32 sin(πt/6) where t is the time (in months), with t=1 corresponding to January (see figure). t (a) What is the period of each function? period of H(t) months period of L(t) months (b) During what part of the year is the difference between the normal high and normal low temperatures greater? spring summer fall winter When is it least? spring summer fall winter

Transcript text: The normal monthly high temperatures $H$ (in degrees Fahrenheit) in Erie, Pennsylvania, are approximated by \[ H(t)=57.54-18.53 \cos \left(\frac{\pi t}{6}\right)-14.03 \sin \left(\frac{\pi t}{6}\right) \] and the normal monthly low temperatures $L$ are approximated by \[ L(t)=42.03-15.99 \cos \left(\frac{\pi t}{6}\right)-14.32 \sin \left(\frac{\pi t}{6}\right) \] where $t$ is the time (in months), with $t=1$ corresponding to January (see figure). $t$ (a) What is the period of each function? period of $H(t)$ $\qquad$ months period of $L(t)$ $\qquad$ months (b) During what part of the year is the difference between the normal high and normal low temperatures gr spring summer fall winter When is it least? spring summer fall winter