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OSCILLATION OF A SPRING A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches. Its motion (in ideal conditions)is modeled by \(y= \frac{1}{4}cos\ 16t\ (t>0)\), where \(y\) is measured in feet and \(t\) is the time in seconds. (a) Graph the function. (b) What is the period of the oscillations? (c) Determine the first time the weight passes the point of equilibrium \((y=0)\).

DATA ANALYSIS The number of hours \(H\) of daylight in Denver, Colorado on the 15th of each month are: \(1(9.67)\), \(2(10.72)\), \(3(11.92)\), \(4(13.25)\), \(5(14.37)\), \(6(14.97)\), \(7(14.72)\), \(8(13.77)\), \(9(12.48)\), \(10(11.18)\), \(11(10.00)\), \(12(9.38)\). The month is represented by \(t\), with \(t=1\) corresponding to January. A model for the data is given by \(H(t)\ =\ 12.13\ +\ 2.77\ sin[(\pi t/6)\ -\ 1.60]\). (a) Use a graphing utility to graph the data points and the model in the same viewing window. (b) What is the period of the model? Is it what you expected? Explain. (c) What is the amplitude of the model? What does it represent in the context of the problem? Explain.

CAPSTONE While walking across flat land, you notice a wind turbine tower of height \(h\) feet directly in front of you. The angle of elevation to the top of the tower is \(A\) degrees. After you walk \(d\) feet closer to the tower, the angle of elevation increases to \(b\) degrees. (a) Draw a diagram to represent the situation. (b) Write an expression for the height \(h\) of the tower in terms of the angles \(A\) and \(B\) and the distance \(d\).

In Exercises 69-74, find the indicated trigonometric value in the specified quadrant. Function \(sin\ \theta\ =\ -\frac{3}{5}\) Quadrant \(IV\) Trigonometric Value \(cos\ \theta\)

THINK ABOUT IT Because \(f(t) = sin t\) and \(g(t) = tan t\) are odd functions, what can be said about the function $h(t)=f(t)g(t)?

In Exercises 69-74, find the indicated trigonometric value in the specified quadrant. Function \(cos\ \theta\ =\ \frac{5}{8}\) Quadrant \(I\) Trigonometric Value \(sec\ \theta\)

GEOMETRY Use a compass to sketch a quarter of a circle of radius 10 centimeters. Using a protractor, construct an angle of \(20^\circ\) in standard position (see figure). Drop a perpendicular line from the point of intersection of the terminal side of the angle and the arc of the circle. By actual measurement, calculate the coordinates \((x, y)\) of the point of intersection and use these measurements to approximate the six trigonometric functions of a \(20^\circ\) angle.

In Exercises 75-90, use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) \(sin\ 10^\circ\)

In Exercises 85-88, convert each angle measure to degrees,minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(-345.12^{\circ}\) (b) \(0.45^{\circ}\)

In Exercises 85-88, convert each angle measure to degrees,minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(2.5^{\circ}\) (b) \(-3.58^{\circ}\)