Chapter 7

Circadian Rhythms Everybody's blood pressure varies over the course of the day. In a certain individual the resting diastolic blood pressure at time \(t\) is given by \(B(t)=80+7 \sin (\pi t / 12),\) where \(t\) is measured in hours since midnight and \(B(t)\) in mmHg (millimeters of mercury). Find this person's diastolic blood pressure at $$ \begin{array}{llll}{\text { (a) } 6 : 00 \text { A.M. }} & {\text { (b) } 10 : 30 \text { A.M. }} & {\text { (c) Noon }} & {\text { (d) } 8 : 00 \text { P.M. }}\end{array} $$

Electric Circuit After the switch is closed in the circuit shown, the current \(t\) seconds later is \(I(t)=0.8 e^{-3 t} \sin 10 t\) . Find the current at the times (a) \(t=0.1 \mathrm{s}\) and (b) \(t=0.5 \mathrm{s}\)

Bungee Jumping A bungee jumper plummets from a high bridge to the river below and then bounces back over and over again. At time \(t\) seconds after her jump, her height \(H\) (in meters) above the river is given by \(H(t)=100+75 e^{-t / 20} \cos \left(\frac{\pi}{4} t\right) .\) Find her height at the times indicated in the table.

Reduction Formulas A reduction formula is one that can be used to "reduce" the number of terms in the input for a trigonometric function. Explain how the figure shows that the following reduction formulas are valid: $$ \sin (t+\pi)=-\sin t \quad \cos (t+\pi)=-\cos t $$ $$ \tan (t+\pi)=\tan t $$