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Magazine Problem 88
In Exercises 69-88, evaluate each expression exactly. $$ \tan \left[2 \cos ^{-1}\left(\frac{5}{13}\right)\right] $$
Problem 89
For each of the following expressions, write an equivalent expression in terms of only the variable \(u\). $$ \cos \left(\sin ^{-1} u\right) $$
Problem 89
For Exercises 87-92, refer to the following: Graphing calculators can be used to find approximate solutions to trigonometric equations. For the equation \(f(x)=g(x)\), let \(Y_{1}=f(x)\) and \(Y_{2}=g(x)\). The \(x\) values that correspond to points of intersections represent solutions. Use a graphing utility to solve the equation \(\sin \theta=\sec \theta\) on \(0 \leq \theta<\pi\).
Problem 90
For Exercises 87-92, refer to the following: Graphing calculators can be used to find approximate solutions to trigonometric equations. For the equation \(f(x)=g(x)\), let \(Y_{1}=f(x)\) and \(Y_{2}=g(x)\). The \(x\) values that correspond to points of intersections represent solutions. Use a graphing utility to solve the equation \(\cos \theta=\csc \theta\) on \(0 \leq \theta<\pi\).
Problem 90
For each of the following expressions, write an equivalent expression in terms of only the variable \(u\). $$ \sin \left(\cos ^{-1} u\right) $$
Problem 91
For Exercises 87-92, refer to the following: Graphing calculators can be used to find approximate solutions to trigonometric equations. For the equation \(f(x)=g(x)\), let \(Y_{1}=f(x)\) and \(Y_{2}=g(x)\). The \(x\) values that correspond to points of intersections represent solutions. Use a graphing utility to find all solutions to the equation \(\sin \theta=e^{\theta}\) for \(\theta \geq 0\).
Problem 91
For each of the following expressions, write an equivalent expression in terms of only the variable \(u\). $$ \tan \left(\cos ^{-1} u\right) $$
Problem 92
For each of the following expressions, write an equivalent expression in terms of only the variable \(u\). $$ \tan \left(\sin ^{-1} u\right) $$
Problem 92
For Exercises 87-92, refer to the following: Graphing calculators can be used to find approximate solutions to trigonometric equations. For the equation \(f(x)=g(x)\), let \(Y_{1}=f(x)\) and \(Y_{2}=g(x)\). The \(x\) values that correspond to points of intersections represent solutions. Use a graphing utility to find all solutions to the equation \(\cos \theta=e^{\theta}\) for \(\theta \geq 0\).
Problem 93
For Exercises 93 and 94 , refer to the following: Annual sales of a product are generally subject to seasonal fluctuations and are approximated by the function $$ s(t)=4.3 \cos \left(\frac{\pi}{6} t\right)+56.2 \quad 0 \leq t \leq 11 $$ where \(t\) represents time in months ( \(t=0\) represents January) and \(s(t)\) represents monthly sales of the product in thousands of dollars. Business. Find the month(s) in which monthly sales are \(\$ 56,200\).
