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The seats of a Ferris wheel are 40 feet from the wheel's center. When you get on the ride, your seat is 5 feet above the ground. How far above the ground are you after rotating through an angle of \(765^{\circ} ?\) Round to the nearest foot.

What is meant by the bearing from point \(O\) to point \(P ?\) Give an example with your description.

In Exercises \(71-74,\) find the length of the arc on a circle of radius \(r\) intercepted by a central angle \(\theta .\) Express arc length in terms of \(\pi .\) Then round your answer to two decimal places. $$Radius, r \quad Central Angle, \theta$$ $$12 inches \quad \theta=45^{\circ}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A wheelchair ramp must be constructed so that the slope is not more than 1 inch of rise for every 1 foot of run, so I used the tangent function to determine the maximum angle that the ramp can make with the ground.

a. Graph the restricted secant function, \(y=\sec x,\) by restricting \(x\) to the intervals \(\left[0, \frac{\pi}{2}\right)\) and \(\left(\frac{\pi}{2}, \pi\right]\) b. Use the horizontal line test to explain why the restricted secant function has an inverse function. c. Use the graph of the restricted secant function to graph \(y=\sec ^{-1} x\).

At a certain time of day, the angle of elevation of the Sun is 40°. To the nearest foot, find the height of a tree whose shadow is 35 feet long.

use reference angles to find the exact value of each expression. Do not use a calculator. $$ \sec 495^{\circ} $$

use reference angles to find the exact value of each expression. Do not use a calculator. $$ \sec 510^{\circ} $$

use reference angles to find the exact value of each expression. Do not use a calculator. $$ \cos \frac{35 \pi}{6} $$

In the theory of biorhythms, sine functions are used to measure a person’s potential. You can obtain your biorhythm chart online by simply entering your date of birth, the date you want your biorhythm chart to begin, and the number of months you wish to have included in the plot. Shown below is your author’s chart, beginning January 25, 2015, when he was 25,473 days old. We all have cycles with the same amplitudes and periods as those shown here. Each of our three basic cycles begins at birth. Use the biorhythm chart shown to solve Exercises 75–82. The longer tick marks correspond to the dates shown. IMAGE CANNOT COPY! The number of hours of daylight in Boston is given by \(y=3 \sin \frac{2 \pi}{365}(x-79)+12\) where \(x\) is the number of days after January 1 . a. What is the amplitude of this function? b. What is the period of this function? c. How many hours of daylight are there on the longest day of the year? d. How many hours of daylight are there on the shortest day of the year? e. Graph the function for one period, starting on January \(1 .\)