91Ó°ÊÓ

What is the amplitude of the sine function? What does this tell you about the graph?

Stonehenge, the famous "stone circle" in England, was built between 2750 B.C. and 1300 B.C. using solid stone blocks weighing over \(99,000\) pounds each. It required 550 people to pull a single stone up a ramp inclined at a \(9^{\circ}\) angle. Describe how right triangle trigonometry can be used to determine the distance the 550 workers had to drag a stone in order to raise it to a height of 30 feet.

The figure shows a highway sign that warns of a railway crossing. The lines that form the cross pass through the circle's center and intersect at right angles. If the radius of the circle is 24 inches, find the length of each of the four arcs formed by the cross. Express your answer in terms of \(\pi\) and then round to two decimal places.

What does a phase shift indicate about the graph of a sine function? How do you determine the phase shift from the function’s equation?

Your neighborhood movie theater has a 25 -foot-high screen located 8 feet above your eye level. If you sit too close to the screen, your viewing angle is too small, resulting in a distorted picture. By contrast, if you sit too far back, the image is quite small, diminishing the movie's visual impact. If you sit \(x\) feet back from the screen, your viewing angle, \(\theta,\) is given by $$\theta=\tan ^{-1} \frac{33}{x}-\tan ^{-1} \frac{8}{x}$$ (GRAPH CANNOT COPY) Find the viewing angle, in radians, at distances of 5 feet, 10 feet, 15 feet, 20 feet, and 25 feet.

How do we measure the distance between two points, \(A\) and \(B,\) on Earth? We measure along a circle with a center, \(C,\) at the center of Earth. The radius of the circle is equal to the distance from \(\mathrm{C}\) to the surface. Use the fact that Earth is a sphere of radius equal to approximately 4000 miles to solve Exercises 93-96. If two points, \(A\) and \(B\), are \(10,000\) miles apart, express angle \(\theta\) in radians and in degrees.

In Exercises 95–96, write the equation for a cosecant function satisfying the given conditions. $$ \text { period: } 3 \pi ; \text { range: }(-\infty,-2] \cup[2, \infty) $$

Standing under this arch, I can determine its height by measuring the angle of elevation to the top of the arch and my distance to a point directly under the arch.

let $$ f(x)=\sin x, g(x)=\cos x, \text { and } h(x)=2 x $$ Find the exact value of each expression. Do not use a calculator. the average rate of change of \(f\) from \(x_{1}=\frac{5 \pi}{4}\) to \(x_{2}=\frac{3 \pi}{2}\)

The angular speed of a point on Earth is \(\frac{\pi}{12}\) radian per hour. The Equator lies on a circle of radius approximately 4000 miles. Find the linear velocity, in miles per hour, of \(\overline{\mathbf{a}}\) point on the Equator.