91Ó°ÊÓ

WRITING Explain why there is more than one tangent function whose graph passes through the origin and has asymptotes at \(x=-\pi\) and \(x=\pi\).

A rock climber is using a rock climbing treadmill that is 10 feet long. The climber begins by lying horizontally on the treadmill, which is then rotated about its midpoint by \(110^{\circ}\) so that the rock climber is climbing toward the top. If the midpoint of the treadmill is 6 feet above the ground, how high above the ground is the top of the treadmill?

A Ferris wheel has a radius of 75 feet. You board a car at the bottom of the Ferris wheel, which is 10 feet above the ground, and rotate \(255^{\circ}\) counterclockwise before the ride temporarily stops. How high above the ground are you when the ride stops? If the radius of the Ferris wheel is doubled, is your height above the ground doubled? Explain your reasoning.

Your school's marching band is performing at halftime during a football game. In the last formation, the band members form a circle 100 feet wide in the center of the field. You start at a point on the circle 100 feet from the goal line, march \(300^{\circ}\) around the circle, and then walk toward the goal line to exit the field. How far from the goal line are you at the point where you leave the circle?

MODELING WITH MATHEMATICS Katoomba Scenic Railway in Australia is the steepest railway in the world. The railway makes an angle of about 52° with the ground. The railway extends horizontally about 458 feet. What is the height of the railway

CRITICAL THINKING Write \(\tan \theta\) as the ratio of two other trigonometric functions. Use this ratio to explain why \(\tan 90^{\circ}\) is undefined but \(\cot 90^{\circ}=0\).

MODELING WITH MATHEMATICS You are standing on the Grand View Terrace viewing platform at Mount Rushmore, 1000 feet from the base of the monument. Not drawn to scale 24° b 1000 ft a. You look up at the top of Mount Rushmore at an angle of 24°. How high is the top of the monument from where you are standing? Assume your eye level is 5.5 feet above the platform. b. The elevation of the Grand View Terrace is 5280 feet. Use your answer in part (a) to fi nd the elevation of the top of Mount Rushmore.

MODELING WITH MATHEMATICS You are standing 120 feet from the base of a 260-foot building. You watch your friend go down the side of the building in a glass elevator. a. Write an equation that gives the distance \(d\) (in feet) your friend is from the top of the building as a function of the angle of elevation \(\theta\). b. Graph the function found in part (a). Explain how the graph relates to this situation.

Your friend claims that the only solution to the trigonometric equation \(\tan \theta=\sqrt{3}\) is \(\theta=60^{\circ}\). Is your friend correct? Explain your reasoning.

WRITING Write a real-life problem that can be solved using a right triangle. Then solve your problem.