Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 7 Applications of Trigonometry.

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Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 7 Applications of Trigonometry

7 Chapter Outline 7.1Oblique Triangles and the Law of Sines 7.2The Law of Cosines; The Area of a Triangle 7.3Vectors and Vector Diagrams 7.4Vector Applications and the Dot Product 7.5Complex Numbers in Trigonometric Form 7.6De Moivre’s Theorem and the Theorem of nth Roots 1-2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Learning Objectives In Section 7.1 you will learn how to:  A.Develop the law of sines, and use it to solve ASA and AAS triangles  B.Solve SSA triangles (the ambiguous case) using the law of sines  C.Use the law of sines to solve applications 7.1 Oblique Triangles and the Law of Sines 1-3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1-6 EXAMPLE 1 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 7.2 you will learn how to:  A.Apply the law of cosines when two sides and an included angle are known (SAS)  B.Apply the law of cosines when three sides are known (SSS)  C.Solve applications using the law of cosines  D.Use trigonometry to find the area of a rectangle 7.2 The Law of Cosines; The Area of a Triangle 1-19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 7.3 you will learn how to:  A.Represent a vector quantity geometrically  B.Represent a vector quantity graphically  C.Perform defined vector operations  D.Represent a vector quantity algebraically and find unity vectors  E.Use vector diagrams to solve applications 7.3Vectors and Vector Diagrams 1-32 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1-52 EXAMPLE 9 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 7.4 you will learn how to:  A.Use vectors to investigate forces in equilibrium  B.Find the components of one vector along another  C.Solve applications involving work  D.Compute dot products and the angle between two vectors  E.Find the projection of one vector along another and resolve a vector into orthogonal components  F.Use vectors for nonvertical projectile motion, and solve related applications 7.4 Vector Applications and the Dot Product 1-54 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 7.5 you will learn how to:  A.Graph a complex number  B.Write a complex number in trigonometric form  C.Convert from trigonometric to rectangular form  D.Interpret products and quotients geometrically  E.Compute products and quotients in trigonometric form  F.Solve applications involving complex numbers (optional) 7.5 Complex Numbers in Trigonometric Form 1-76 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 7.6 you will learn how to:  A.Using De Moivre’s theorem to raise complex numbers to any power  B.Use De Moivre’s theorem to check solutions to polynomial equations  C.Use the nth roots theorem to find the nth roots of a complex number 7.6 De Moivre’s Theorem and the Theorem of nth Roots 1-91 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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