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Angles and Applications | |
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Introduction | |
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Plane Angle | |
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Measures of Angles | |
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Arc Length | |
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Lengths of Arcs on a Unit Circle | |
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Area of a Sector | |
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Linear and Angular Velocity | |
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Trigonometric Functions of a General Angle | |
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Coordinates on a Line | |
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Coordinates in a Plane | |
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Angles in Standard Position | |
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Trigonometric Functions of a General Angle | |
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Quadrant Signs of the Functions | |
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Trigonometric Functions of Quadrantal Angles | |
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Undefined Trigonometric Functions | |
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Coordinates of Points on a Unit Circle | |
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Circular Functions | |
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Trigonometric Functions of an Acute Angle | |
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Trigonometric Functions of an Acute Angle | |
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Trigonometric Functions of Complementary Angles | |
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Trigonometric Functions of 30�, 45�, and 60� | |
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Trigonometric Function Values | |
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Accuracy of Results Using Approximations | |
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Selecting the Function in Problem-Solving | |
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Angles of Depression and Elevation | |
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Solution of Right Triangles | |
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Introduction | |
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Four-Place Tables of Trigonometric Functions | |
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Tables of Values for Trigonometric Functions | |
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Using Tables to Find an Angle Given a Function Value | |
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Calculator Values of Trigonometric Functions | |
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Find an Angle Given a Function Value Using a Calculator | |
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Accuracy in Computed Results | |
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Practical Applications | |
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Bearing | |
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Vectors | |
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Vector Addition | |
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Components of a Vector | |
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Air Navigation | |
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Inclined Plane | |
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Reduction to Functions of Positive Acute Angles | |
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Coterminal Angles | |
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Functions of a Negative Angle | |
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Reference Angles | |
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Angles with a Given Function Value | |
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Variations and Graphs of the Trigonometric Functions | |
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Line Representations of Trigonometric Functions | |
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Variations of Trigonometric Functions | |
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Graphs of Trigonometric Functions | |
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Horizontal and Vertical Shifts | |
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Periodic Functions | |
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Sine Curves | |
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Basic Relationships and Identities | |
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Basic Relationships | |
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Simplification of Trigonometric Expressions | |
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Trigonometric Identities | |
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Trigonometric Functions of Two Angles | |
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Addition Formulas | |
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Subtraction Formulas | |
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Double-Angle Formulas | |
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Half-Angle Formulas | |
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Sum, Difference, and Product Formulas | |
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Products of Sines and Cosines | |
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Sum and Difference of Sines and Cosines | |
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Oblique Triangles | |
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Oblique Triangles | |
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Law of Sines | |
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Law of Cosines | |
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Solution of Oblique Triangles | |
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Area of a Triangle | |
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Area of a Triangle | |
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Area Formulas | |
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Inverses of Trigonometric Functions | |
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Inverse Trigonometric Relations | |
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Graphs of the Inverse Trigonometric Relations | |
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Inverse Trigonometric Functions | |
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Principal-Value Range | |
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General Values of Inverse Trigonometric Relations | |
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Trigonometric Equations | |
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Trigonometric Equations | |
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Solving Trigonometric Equations | |
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Complex Numbers | |
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Imaginary Numbers | |
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Complex Numbers | |
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Algebraic Operations | |
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Graphic Representation of Complex Numbers | |
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Graphic Representation of Addition and Subtraction | |
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Polar or Trigonometric Form of Complex Numbers | |
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Multiplication and Division in Polar Form | |
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De Moivre's Theorem | |
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Roots of Complex Numbers | |
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Geometry | |
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Introduction | |
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Angles | |
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Lines | |
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Triangles | |
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Polygons | |
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Circles | |
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Tables | |
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Trigonometric Functions-Angle in 10-Minute Intervals | |
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Trigonometric Functions-Angle in Tenth of Degree Intervals | |
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Trigonometric Functions-Angle in Hundredth of Radian Intervals | |
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Index | |