Analytic Trigonometry with Applications

Analytic Trigonometry with Applications

Raymond A. Barnett

Language: English

Pages: 624

ISBN: 0470648058

Format: PDF / Kindle (mobi) / ePub


Barnett, Analytic Trigonometry is a text that students can actually read, understand, and apply. Concept development moves from the concrete to abstract to engage the student. Almost every concept is illustrated by an example followed by a matching problem allowing students to practice knowledge precisely when they acquire it. To gain student interest quickly, the text moves directly into trigonometric concepts and applications and reviews essential material from prerequisite courses only as needed. Extensive chapter review summaries, chapter and cumulative review exercises with answers keyed to the corresponding text sections, effective use of color comments and annotations, and prominent displays of important material all help the student master the subject. Analytic Trigonometry 11th edition includes updated applications from a range of different fields to convince all students that trigonometry is really useful.

The seamless integration of Barnett, Analytical Trigonometry 11th edition with WileyPLUS, a research-based, online environment for effective teaching and learning, builds student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right.

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Left and to the right. Figure 2 illustrates how y = sin x = b varies as x increases from 0 to 2p and P = (a, b) moves around the unit circle. q b P = (a, b) (0, 1) 1 x b p a 0 a 2p (1, 0) w FIGURE 2 y = sin x = b As x increases y = sin x = b from 0 to p>2 increases from 0 to 1 from p>2 to p decreases from 1 to 0 from p to 3p>2 decreases from 0 to - 1 from 3p>2 to 2p increases from - 1 to 0 The information in Figure 2 can be translated into a graph of y = sin x for x between 0.

Modeling Sea Temperatures Repeat Problem 79 for the data from Buoy 44004. Figure for 78 81. Modeling Gas Storage The Energy Information Administration (EIA) maintains data for the natural gas stored in underground facilities. Table 6 lists the monthly working natural gas storage for the eastern and the western regions of the United States from July 2005 to June 2007 in billions of cubic feet (Bcf). Find a model of the form g = k + A sin Bx for the data from the eastern region. Graph the model.

And Phase Shift Find the period and phase shift for y = sin(2x + p/2). Solution Method I The graph will cover one full period as the input of sine, 2x + p/2, varies from 0 to 2p. Find the corresponding x values: p p 2x + = 0 2x + = 2p 2 2 p p 2x = 2x = + 2p 2 2 p p 3p x = x = + p or 4 4 4 Phase shift The phase shift is -p/4, and the period is p. Period 3.3 Graphing y = k + A sin(Bx + C) and y = k + A cos(Bx + C) 159 Method II Using the formulas developed above, the period is 2p>B and the.

Provides the moon’s phases (percent visible) in terms of number of days after 01/01/2012, 12 A.M. CST. TABLE 1 Lunar Phases Phase Days after 01/01/12 100% (full moon) 9.06 50% 16.44 0% (new moon) 23.83 50% 31.21 100% (full moon) 38.59 (A) Use the information in the table to find a function of the form y = k + A cos(Bx + C) that models the lunar phases in terms of days after 01/01/12, 12 A.M. CST. Round all constants to three significant digits. 3.3 Graphing y = k + A sin(Bx + C).

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