The data show the average monthly temperatures for

Chapter 4, Problem 4.5.115

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The data show the average monthly temperatures for Washington, D.C. c -2p, 2p, 3-2, 2, 14 p 2 d y = sin x - sin 3x 9 + sin 5x 25 c -2p, 2p, 3-2, 2, 14 p 2 d y = sin x + sin 2x 2 + sin 3x 3 + sin 4x 4 112. When graphing one complete cycle of I find it easiest to begin my graph on the 113. Using the equation if I replace either or with its opposite, the graph of the resulting equation is a reflection of the graph of the original equation about the 114. A ride on a circular Ferris wheel is like riding sinusoidal graphs. 115. Determine the range of each of the following functions. Then give a viewing rectangle, or window, that shows two periods of the function s graph. a. b. 116. Write the equation for a cosine function with amplitude period 1, and phase shift In Chapter 5, we will prove the following identities: Use these identities to solve Exercises 117 118. 117. Use the identity for to graph one period of 118. Use the identity for to graph one period of Group Exercise 119. This exercise is intended to provide some fun with biorhythms, regardless of whether you believe they have any validity. We will use each member s chart to determine biorhythmic compatibility. Before meeting, each group member should go online and obtain his or her biorhythm chart. The date of the group meeting is the date on which your chart should begin. Include 12 months in the plot. At the meeting, compare differences and similarities among the intellectual sinusoidal curves. Using these comparisons, each person should find the one other person with whom he or she would be most intellectually compatible. Preview Exercises Exercises 120 122 will help you prepare for the material covered in the next section. 120. Solve: 121. Simplify: 122. a. Graph b. Consider the reciprocal function of namely, What does your graph from part (a) indicate about this reciprocal function for x = -p, p, 3p, and 5p? y = -3 sec x 2 . y = -3 cos x 2 , y = -3 cos x 2 for -p x 5p. - 3p 4 + p 4 2 . - p 2 6 x + p 4 6 p 2 . y = cos2 x. cos2 x y = sin2 sin x. 2 x cos2 x = 1 2 + 1 2 cos 2x. sin2 x = 1 2 - 1 2 cos 2x -2. p, g1x2 = sin 3ax + p 6 b - 2 f1x2 = 3 sinax + p 6 b - 2 x-axis. y = A sin Bx, BA x-axis. y = A cos 1Bx - C2, x (Month) Average Monthly Temperature, F 1 (January) 34.6 2 (February) 37.5 3 (March) 47.2 4 (April) 56.5 5 (May) 66.4 6 (June) 75.6 7 (July) 80.0 8 (August) 78.5 9 (September) 71.3 10 (October) 59.7 11 (November) 49.8 12 (December) 39.4 Source: U.S. National Oceanic and Atmospheric Administration a. Use your graphing utility to draw a scatter plot of the data from through b. Use the SINe REGression feature to find the sinusoidal function of the form that best fits the data. c. Use your graphing utility to draw the sinusoidal function of best fit on the scatter plot.