Ebook Algebra and Trigonometry (Eighth edition): Part 2

Ebook Algebra and Trigonometry (Eighth edition): Part 2 presents the following content: Trigonometry; Analytic Trigonometry; Additional Topics in Trigonometry; Systems of Equations and Inequalities; Matrices and Determinants; Sequences, Series, and Probability.
Nội dung trích xuất từ tài liệu:
Ebook Algebra and Trigonometry (Eighth edition): Part 2 Trigonometry 6.1 Angles and Their Measure 6 6.2 Right Triangle Trigonometry 6.3 Trigonometric Functions of Any Angle 6.4 Graphs of Sine and Cosine Functions 6.5 Graphs of Other Trigonometric Functions 6.6 Inverse Trigonometric Functions 6.7 Applications and Models In Mathematics Trigonometry is used to find relationships between the sides and angles of triangles, and to write trigonometric functions as models of real-life quantities. In Real Life Trigonometric functions are used to model quantities that are periodic. For instance, throughout the day, the depth of water at the end of a dock in Bar Harbor, Maine varies with the tides. The depth can be modeled by a trigonometric function. (See Example 7, page 485.) Andre Jenny/Alamy IN CAREERS There are many careers that use trigonometry. Several are listed below. • Biologist • Mechanical Engineer Exercise 68, page 465 Exercise 95, page 499 • Meteorologist • Surveyor Exercise 105, page 477 Exercise 41, page 519 443 444 Chapter 6 Trigonometry 6.1 ANGLES AND THEIR MEASURE What you should learn Angles • Describe angles. • Use degree measure. As derived from the Greek language, the word trigonometry means “measurement of triangles.” Initially, trigonometry dealt with relationships among the sides and angles of • Use radian measure. triangles and was used in the development of astronomy, navigation, and surveying. • Convert between degree and With the development of calculus and the physical sciences in the 17th century, a radian measures. different perspective arose—one that viewed the classic trigonometric relationships as • Use angles to model and solve functions with the set of real numbers as their domains. Consequently, the applications real-life problems. of trigonometry expanded to include a vast number of physical phenomena involving Why you should learn it rotations and vibrations. These phenomena include sound waves, light rays, planetary orbits, vibrating strings, pendulums, and orbits of atomic particles. You can use angles to model and solve real-life problems. For instance, in The approach in this text incorporates both perspectives, starting with angles and Exercise 116 on page 455, you can use their measure. angles to find the speed of a bicycle. y id e in al s Terminal m side Ter Vertex x Initial side Ini tia l si de Angle Angle in standard position FIGURE 6.1 FIGURE 6.2 © Wolfgang/Rat ...