Exam 9: Trigonometric Identities, Models, and Complex Numbers

If $-\frac{\pi}{2} \leq t \leq \frac{\pi}{2}$ , in what quadrant is $\sin t=0.61$ ?

Graph $y=\cos t$ and use that graph to approximate the solution of $0.12=\cos t$ on $0 \leq t \leq \frac{\pi}{2}$ . Give $t$ in degrees to 2 decimal places.

How many solutions does $\cos ^{3} x+\cos x \sin ^{2} x=4 \sin x$ have for $-\pi \leq x \leq 2 \pi$ ?

The following table gives $A(t)$ , the percentage of the electorate favoring candidate $A$ during the 12 months preceding a presidential election. Time, $t$ , is measured in months, and $t=0$ is a year before election day. Assume that $A(t)$ is approximately trigonometric. A second candidate, candidate $B$ , has a percentage of candidate support given by $B(t)=31+15 \sin \left(\frac{\pi}{6} t\right)$ . Let $f(t)=A(t)+B(t)$ for $0 \leq t \leq 12$ . What is the meaning of the minimum of $f(t)$ ?

A ferris wheel sitting on the ground is 18 meters in diameter and makes one revolution every 5 minutes. If you start in the 9 o'clock position $t=0$ and the wheel is rotating clockwise, write a formula for your height above the ground at time $t$ .

Does $\sin u+\sin v=2 \sin \left(\frac{u-v}{2}\right) \cos \left(\frac{u+v}{2}\right)$ ?