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Chapter 5: Problem 101
What is an angle?
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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 \(\theta=10^{\circ},\) find the distance between \(A\) and \(B\) to the nearest mile.
We will prove the following identities: $$\begin{array}{l} {\sin ^{2} x=\frac{1}{2}-\frac{1}{2} \cos 2 x} \\ {\cos ^{2} x=\frac{1}{2}+\frac{1}{2} \cos 2 x} \end{array}$$ Use the identity for \(\cos ^{2} x\) to graph one period of \(y=\cos ^{2} x\)
Without drawing a graph, describe the behavior of the graph of \(y=\cos ^{-1} x .\) Mention the function's domain and range in your description.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Determine the range of each of the following functions Then give a viewing rectangle, or window, that shows two periods of the function's graph. a. $$f(x)=3 \sin \left(x+\frac{\pi}{6}\right)-2$$ b. $$g(x)=\sin 3\left(x+\frac{\pi}{6}\right)-2$$
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.
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