91Ó°ÊÓ

\(\cot 2 \theta=1\)

For each of the following equations, solve for (a) all degree solutions and (b) \(\theta\) if \(0^{\circ} \leq \theta<360^{\circ}\). Use a calculator to approximate all answers to the nearest tenth of a degree. $$ 2 \cos \theta-5=3 \cos \theta-2 $$

\(\cos 3 \theta=-1\)

\(\sin 10 \theta=\frac{\sqrt{3}}{2}\)

\(\tan 2 x=1\)

Use the quadratic formula to find (a) all degree solutions and (b) \(\theta\) if \(0^{\circ} \leq \theta<360^{\circ}\). Use a calculator to approximate all answers to the nearest tenth of a degree. $$ 2 \sin ^{2} \theta-2 \sin \theta-1=0 $$

Ferris Wheel The Ferris wheel built in Vienna in 1897 has a diameter of 197 feet and sits 12 feet above the ground. It rotates in a counterclockwise direction, making one complete revolution every 15 minutes. Use parametric equations to model the path of a rider on this wheel. Place your coordinate system so that the origin of the coordinate system is on the ground below the bottom of the wheel. You want to end up with parametric equations that will give you the position of the rider every minute of the ride. Graph your results on a graphing calculator.

Human Cannonball A human cannonball is fired from a cannon with an initial velocity of 50 miles per hour. On the same screen on your calculator, graph the paths taken by the cannonball if the angle between the cannon and the horizontal is \(20^{\circ}, 30^{\circ}, 40^{\circ}, 50^{\circ}, 60^{\circ}, 70^{\circ}\), and \(80^{\circ}\).

\(\tan ^{2} 3 \theta=3\)

Find all radian solutions to the following equations. $$ \sin \left(A+\frac{\pi}{12}\right)=-\frac{1}{\sqrt{2}} $$