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Chapter 5: Problem 27
Write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression. $$\frac{\tan 10^{\circ}+\tan 35^{\circ}}{1-\tan 10^{\circ} \tan 35^{\circ}}$$
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Solve and graph the solution set on a number line: $$\frac{2 x-3}{8} \leq \frac{3 x}{8}+\frac{1}{4}$$ (Section P.9, Example 5 )
Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$\cos x \csc x=2 \cos x$$
Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$\cos ^{2} x+5 \cos x-1=0$$
A city's tall buildings and narrow streets reduce the amount of sunlight. If \(h\) is the average height of the buildings and \(w\) is the width of the street, the angle of elevation from the street to the top of the buildings is given by the trigonometric equation $$\tan \theta=\frac{h}{w}$$ A value of \(\theta=63^{\circ}\) can result in an \(85 \%\) loss of illumination. Some people experience depression with loss of sunlight. Determine whether such a person should live on a city street that is 80 feet wide with buildings whose heights average 400 feet. Explain your answer and include \(\theta,\) to the nearest degree, in your argument.
Find the exact value of each expression. Do not use a calculator. $$\sin \left[\sin ^{-1} \frac{3}{5}-\cos ^{-1}\left(-\frac{4}{5}\right)\right]$$
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