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Chapter 1: Problem 65
Convert the angle measure from radians to degrees. Round to three decimal places. $$\frac{15 \pi}{8}$$
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A photographer is taking a picture of a three-foot-tall painting hung in an art gallery. The camera lens is 1 foot below the lower edge of the painting (see figure). The angle \(\beta\) subtended by the camera lens \(x\) feet from the painting is $$ \beta=\arctan \frac{3 x}{x^{2}+4}, \quad x>0 $$ (a) Use a graphing utility to graph \(\beta\) as a function of \(x\). (b) Move the cursor along the graph to approximate the distance from the picture when \(\beta\) is maximum. (c) Identify the asymptote of the graph and discuss its meaning in the context of the problem.
In Exercises 19-34, use a calculator to evaluate the expression. Round your result to two decimal places. $$ \arctan 0.92 $$
Use a graphing utility to graph the functions \(f(x)=\sqrt{x}\) and \(g(x)=6
\arctan x\)
For \(x>0\), it appears that \(g>f\). Explain why you know that there exists a
positive real number \(a\) such that \(g
$$ \text { In Exercises 49-58, find the exact value of the expression. } $$ $$ \cos \left(\arcsin \frac{5}{13}\right) $$
In Exercises 19-34, use a calculator to evaluate the expression. Round your result to two decimal places. $$ \tan ^{-1}\left(-\frac{95}{7}\right) $$
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