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Chapter 5: Problem 86
Determine whether the statement is true or false. Justify your answer. $$\sec 30^{\circ}=\csc 60^{\circ}$$
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Equation of a Line in Standard Write the standard form of the equation of the line that has the specified characteristics. \(m=-\frac{1}{2},\) passes through \(\left(\frac{1}{3}, 0\right)\)
The normal daily high temperature \(T\) (in degrees Fahrenheit) in Savannah, Georgia, can be approximated by $$T=76.4+16 \cos \left(\frac{\pi t}{6}-\frac{7 \pi}{6}\right)$$ where \(t\) is the time (in months), with \(t=1\) corresponding to January. Find the normal daily high temperature for each month. (Source: National Climatic Data Center) (a) January (b) July (c) October
(a) Use a graphing utility to complete the table. Round your results to four decimal places. $$\begin{array}{|l|l|l|l|l|l|}\hline \theta & 0^{\circ} & 20^{\circ} & 40^{\circ} & 60^{\circ} & 80^{\circ} \\\\\hline \sin \theta & & & & & \\\\\hline \cos \theta & & & & & \\\\\hline \tan \theta & & & & & \\\\\hline\end{array}$$ (b) Classify each of the three trigonometric functions as increasing or decreasing for the table values. (c) From the values in the table, verify that the tangent function is the quotient of the sine and cosine functions.
Finding the Domain of a Function Find the domain of the function. $$g(x)=\sqrt{7-x}$$
Solve the equation. Round your answer to three decimal places, if necessary. $$x^{2}-2 x-5=0$$
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