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Chapter 4: Problem 33
Suppose a slice of a 12 -inch pizza has an area of 20 square inches. What is the angle of this slice?
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For Exercises \(29-34,\) assume the surface of the earth is a sphere with radius 3963 miles. The latitude of \(a\) point \(P\) on the earth's surface is the angle between the line from the center of the earth to \(P\) and the line from the center of the earth to the point on the equator closest to \(P\), as shown below for latitude \(40^{\circ} .\) Dallas has latitude \(32.8^{\circ}\) north. Find the radius of the circle formed by the points with the same latitude as Dallas.
Suppose \(-\frac{\pi}{2}<\theta<0\) and \(\cos \theta=0.1\). Evaluate \(\sin \theta\).
Find the perimeter of an isosceles triangle that has two sides of length 8 and a \(130^{\circ}\) angle between those two sides.
Suppose \(n\) is an integer. Find formulas for \(\sec (\theta+n \pi), \csc (\theta+n \pi)\), and \(\cot (\theta+n \pi)\) in terms of \(\sec \theta, \csc \theta,\) and \(\cot \theta\).
Find the smallest positive number \(x\) such that $$ (\tan x)\left(1+2 \tan \left(\frac{\pi}{2}-x\right)\right)=2-\sqrt{3} $$
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