91Ó°ÊÓ

For each problem below, a point is rotating with uniform circular motion on a circle of radius \(r\). $$ \text { Find } v \text { if } r=2 \text { inches and } \omega=5 \mathrm{rad} / \mathrm{sec} \text {. } $$

Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5 . Trace the circle to find the sine and cosine of each angle to the nearest ten-thousandth. \(120^{\circ}\)

For each angle below, a. Draw the angle in standard position. b. Convert to degree measure. c. Label the reference angle in both degrees and radians. $$\frac{7 \pi}{3}$$

Radius of a Circle If the sector formed by a central angle of \(30^{\circ}\) has an area of \(\pi / 3\) square centimeters, find the radius of the circle.

Velocity of a Ferris Wheel Use Figure 7 as a model of the Ferris wheel called Colossus that was built in St. Louis in 1986. The diameter of the wheel is 165 feet. A brochure that gives some statistics associated with Colossus indicates that it rotates at \(1.5\) revolutions per minute and also indicates that a rider on the wheel is traveling at 10 miles per hour. Explain why these two numbers, \(1.5\) revolutions per minute and 10 miles per hour, cannot both be correct.

Use a calculator to find \(\theta\) to the nearest tenth of a degree, if \(0^{\circ}<\theta<360^{\circ}\) and $$ \tan \theta=0.5890 \text { with } \theta \text { in QI } $$

Windshield Wiper An automobile windshield wiper 10 inches long rotates through an angle of \(60^{\circ}\). If the rubber part of the blade covers only the last 9 inches of the wiper, find the area of the windshield cleaned by the windshield wiper.

Use a calculator to find \(\theta\) to the nearest tenth of a degree, if \(0^{\circ}<\theta<360^{\circ}\) and $$ \cos \theta=0.2644 \text { with } \theta \text { in QIV } $$

Identify the argument of each function. \(\tan \left(\frac{x}{2}+\frac{\pi}{8}\right)\)

Angle of Depression A man standing on the roof of a building \(86.0\) feet above the ground looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be \(14.5^{\circ}\), while the angle of depression from the roof of his building to the bottom of the building next door is \(43.2^{\circ}\). How tall is the building next door?