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Chapter 4: Problem 42
Determine the quadrant in which each angle lies. (a) \(8.3^{\circ}\) (b) \(257^{\circ} 30^{\prime}\)
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Use a graphing utility to graph the two equations in the same viewing window. Use the graphs to determine whether the expressions are equivalent. Verify the results algebraically. $$ y_{1}=1+\cot ^{2} x, \quad y_{2}=\csc ^{2} x $$
Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\). (a) As \(x \rightarrow 0^{+}\), the value of \(f(x) \rightarrow\) (b) As \(x \rightarrow 0^{-}\), the value of \(f(x) \rightarrow\) (c) As \(x \rightarrow \pi^{+}\), the value of \(f(x) \rightarrow\) (d) As \(x \rightarrow \pi^{-}\), the value of \(f(x) \rightarrow\) $$ f(x)=\csc x $$
The projected monthly sales \(S\) (in thousands of units) of lawn mowers (a seasonal product) are modeled by \(S=74+3 t-40 \cos (\pi t / 6),\) where \(t\) is the time (in months), with \(t=1\) corresponding to January. Graph the sales function over 1 year.
Evaluate the expression without using a calculator. $$ \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) $$
Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically. $$ f(x)=x^{2}-\sec x $$
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