675 CHAPTER 6 Review Exercises Graph each function over a one-period interval. 79. y = 3 sin x 80. y = 1 2 sec x 81. y = -tan x 82. y = -2 cos x 83. y = 2 + cot x 84. y = -1 + csc x 85. y = sin 2x 86. y = tan 3x 87. y = 3 cos 2x 88. y = 1 2 cot 3x 89. y = cos ax - p 4b 90. y = tan ax - p 2b 91. y = sec a2x + p 3b 92. y = sin a3x + p 2b 93. y = 1 + 2 cos 3x 94. y = -1 - 3 sin 2x 95. y = 2 sin px 96. y = - 1 2 cos1px - p2 (Modeling) Monthly Temperatures A set of temperature data (in °F) is given for a particular location. (Data from www.weatherbase.com) (a) Plot the data over a two-year interval. (b) Use sine regression to determine a model for the two-year interval. Let x = 1 represent January of the first year. (c) Graph the equation from part (b) together with the given data on the same coordinate axes. 97. Average Monthly Temperature, Auckland, New Zealand Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec 67.6 68.5 65.8 61.3 57.2 53.2 51.6 52.9 55.4 58.1 61.2 64.9 98. Average Low Temperature, Auckland, New Zealand Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec 60.8 61.7 58.8 54.9 51.1 47.1 45.5 46.8 49.5 52.2 55.0 58.8 Connecting Graphs with Equations Determine the simplest form of an equation for each graph. Choose b 70, and include no phase shifts. 99. x y 0 1 2 –1 –2 p p 2 2p 3p 2 100. x y 0 1 2 –1 –2 p 4 p p 2 3p 4 101. x y 0 3 –3 –p p p 2 p 2 – 102. x y 0 1 2 –1 p p 2 2p 3p 2 –3
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