Chapter 4: Circular Functions
4-1: Measures of Angles and Rotations
*Convert between degrees, radians, and revolutions.
pp. 236-237 (1-22)
4-2: Lengths of Arcs and Areas of Sectors
*Find lengths of circular arcs, and areas of sectors.
*Solve problems involving lengths of arcs or areas of sectors.
pp. 242 (1-15)
4-3: Sines, Cosines, and Tangents
*Find sines, cosines, and tangents of angles.
*Apply the definitions of the sine, cosine, and tangent functions.
*Use the unit circle to find values of sines, cosines, and tangents.
pp. 248-249 (1-22)
4-4: Basic Identities Involving Sines, Cosines, and Tangents
*Apply the definitions of the sine, cosine, and tangent functions.
*Apply theorems about sines, cosines, and tangents.
pp. 255-256 (1-21)
4-5: Exact Values of Sines, Cosines, and Tangents
*Find sines, cosines, and tangents of angles.
*Apply theorems about sines, cosines, and tangents.
pp. 260-261 (1-15)
4-6: The Sine, Cosine, and Tangent Functions
*Apply the definitions of the sine, cosine, and tangent functions.
*Draw or interpret graphs of the parent sine, cosine, and tangent functions.
pp. 269-271 (1-12)
4-7: Scale-Change Images of Circular Functions
*Identify the amplitude, period, frequency, and other properties of circular functions.
*Use equations of circular functions to solve problems about real phenomena.
*Graph transformation images of circular functions.
*State equations for graphs of circular functions.
pp. 275-277 (1-16)
4-8: Translation Images of Circular Functions
*Identify the amplitude, period, frequency, and other properties of circular functions.
*Use equations of circular functions to solve problems about real phenomena.
*Graph transformation images of circular functions.
*State equations for graphs of circular functions.
pp. 282-284 (1-16)
4-9: The Graph-Standardization Theorem
*Identify the amplitude, period, frequency, and other properties of circular functions.
*Use equations of circular functions to solve problems about real phenomena.
*Graph transformation images of circular functions.
*State equations for graphs of circular functions.
pp. 290-291 (1-13)
4-10: Modeling with Circular Functions
*Find equations of circular functions to model periodic phenomena.
pp. 296-297 (1-10)
The following videos discuss topics which deal with Chapters 4 AND 5:
Chapter 5: Trigonometric Functions
5-1: Trigonometric Ratios in Right Triangles
*Find sines, cosines, and tangents of angles.
*Use trigonometry to find lengths and angles in right triangles.
*Solve problems using trigonometric ratios in right triangles.
pp. 313-315 (1-16)
5-2: The Law of Cosines
*Use trigonometry to find lengths and angles in triangles.
*Interpret the Law of Cosines.
*Solve problems involving the Law of Cosines.
pp. 318-319 (1-14)
5-3: The Inverse Cosine Function
*Evaluate the inverse cosine function.
*Solve equations of the form cos x = k.
*State properties of the inverse cosine function.
*Write and solve equations for phenomena described by cosine functions.
*Graph or identify graphs of the inverse cosine function.
pp. 324-326 (1-18)
5-4: The Law of Sines
*Use trigonometry to find lengths and angles in triangles.
*Interpret the Law of Sines.
*Solve problems involving the Law of Sines.
*Write and solve equations for phenomena described by sine functions.
pp. 331-332 (1-20)
5-5: The Inverse Sine Function
*Evaluate the inverse sine function.
*Solve equations of the form sin x = k.
*State properties of the inverse sine function.
*Write and solve equations for phenomena described by sine functions.
*Graph or identify graphs of the inverse sine function.
pp. 337-339 (1-24)
5-6: The Inverse Tangent Function
*Evaluate the inverse tangent function.
*Solve equations of the form tan x = k.
*State properties of the inverse tangent function.
*Write and solve equations for phenomena described by tangent functions.
*Graph or identify graphs of the inverse tangent function.
pp. 342-343 (1-19)
5-7: General Solutions to Trigonometric Equations
*Solve trigonometric equations.
*Write and solve equations for phenomena described by trigonometric and circular functions.
pp. 350-351 (1-14)
Chapter 11: Matrices and Trigonometry
11-1: Matrix Multiplication
*Multiply matrices when possible.
*Apply properties of matrices and matrix multiplication.
*Use a matrix to organize information.
pp. 701-703 (1-20)
11-2: Matrices for Transformations
*Represent reflections, scale changes, and size changes as matrices.
*Use matrices to find the image of a figure under a transformation.
pp. 707-708 (1-14)
11-3: Matrices for Composites of Transformations
*Apply properties of matrices and matrix multiplication.
*Represent rotations as matrices.
*Represent composites of transformations as matrix products.
*Use matrices to find the image of a figure under a transformation.
pp. 713-715 (1-17)
11-4: The General Rotation Matrix
*Represent reflections, scale changes, and size changes as matrices.
*Represent composites of transformations as matrix products.
*Use matrices to find the image of a figure under a transformation.
pp. 718-719 (1-13)
11-5: Formulas for cos(alpha + beta) and sin(alpha + beta)
*Apply the Addition Formulas for the cosine and sine.
pp. 723-724 (1-19)
11-6: Double-Angle Formulas for cosine and sine
*Apply the Double Angle Formulas for the cosine and sine.
pp. 728-729 (1-20)
11-7: Inverses of 2 X 2 Matrices
*Use matrices to solve systems of equations.
*Find the inverse of a 2 X 2 matrix.
*Apply properties of matrices and matrix multiplication.
pp. 735-736 (1-20)
Chapter 12: Quadratic Relations
12-1: The Geometry of the Ellipse
*State and apply properties of ellipses to draw or describe them.
*Describe the intersections of a plane and a cone of 2 napes.
pp. 757-758 (1-13)
12-2: The Algebra of the Ellipse
*Use properties of ellipses to write equations describing them.
*Determine information about elliptical orbits.
*Graph or identify graphs of ellipses given their equations.
*Graph transformation images of parent ellipses.
pp. 765-767 (1-19)
12-3: The Hyperbola
*Use properties of hyperbolas to write equations describing them.
*State and apply properties of hyperbolas to draw or describe them.
*Graph or identify graphs of hyperbolas given their equations.
*Graph transformation images of parent hyperbolas.
pp. 774-775 (1-15)
12-4: Rotating Relations
*Find equations for rotation images of figures.
*State and apply properties of ellipses and hyperbolas to draw or describe them.
p. 782 (1-12)
12-5: The General Quadratic Equation
*Rewrite equations of conic sections in the general form of a quadratic relation in two variable.
*Describe the intersections of a plane and a cone of 2 napes.
*Graph transformation images of parent ellipses and hyperbolas.
*Describe graphs of quadratic equations.
pp. 790-791 (1-16)
Chapter 13: Further Work with Trigonometry
13-1: The Secant, Cosecant, and Cotangent Functions
*Evaluate the reciprocal trigonometric functions.
*Apply properties of the reciprocal trigonometric functions.
pp. 809-810 (1-21)
13-2: Proving Trigonometric Identities
*Prove trigonometric identities.
*Use an automatic grapher to test a proposed identity.
pp. 814-815 (1-17)
13-3: Restrictions on Identities
*Prove trigonometric identities.
*Describe singularities of functions.
*Use an automatic grapher to test a proposed identity.
pp. 817-818 (1-14)
13-4: Polar Coordinates
*Given polar coordinates of a point, determine its rectangular coordinates, and vice versa.
*Plot points in a polar coordinate system.
pp. 825-826 (1-20)
13-5: Polar Graphs
*Graph and interpret graphs of polar equations.
pp. 831-832 (1-14)
13-6: The Geometry of Complex Numbers
*Represent complex numbers in different forms.
*Graph complex numbers.
pp. 835-836 (1-16)
13-7: Trigonometric Form of Complex Numbers
*Perform operations with complex numbers in polar or trigonometric form.
*Represent complex numbers in different forms.
*Graph complex numbers.
pp. 843-844 (1-19)
13-8: DeMoivre's Theorem
*Find powers and roots of complex numbers.
p. 850 (1-14)