 Chapter 1: Chapter 1 Review Exercises
 Chapter 1.1: Angles
 Chapter 1.11.2: Quiz
 Chapter 1.2: Trigonometric Functions
 Chapter 1.3: Trigonometric Functions
 Chapter 1.4: Using the Definitions of the Trigonometric Functions
 Chapter 2: Chapter 2 Review Exercises
 Chapter 2.1: Trigonometric Functions of Acute Angles
 Chapter 2.12.3: Quiz
 Chapter 2.2: Trigonometric Functions of NonAcute Angles
 Chapter 2.3: Finding Trigonometric Function Values Using a Calculator
 Chapter 2.4: Solving Right Triangles
 Chapter 2.5: Further Applications of Right Triangles
 Chapter 3: Review Exercises
 Chapter 3.1: Radian Measure
 Chapter 3.1  3.3: Quiz
 Chapter 3.2: Applications of Radian Measure
 Chapter 3.3: The Unit Circle and Circular Functions
 Chapter 3.4: Linear and Angular Speed
 Chapter 4: Review Exercises
 Chapter 4.1: Graphs of the Sine and Cosine Functions
 Chapter 4.1  4.2: Quiz
 Chapter 4.2: Translations of the Graphs of the Sine and Cosine Functions
 Chapter 4.3: Graphs of the Tangent and Cotangent Functions
 Chapter 4.4: Graphs of the Secant and Cosecant Functions
 Chapter 4.5: Harmonic Motion
 Chapter 5: Review Exercise
 Chapter 5.1: Fundamental Identities
 Chapter 5.1  5.4: Quiz
 Chapter 5.2: Verifying Trigonometric Identities
 Chapter 5.3: Sum and Difference Identities for Cosine
 Chapter 5.4: Sum and Difference Identities for Sine and Tangent
 Chapter 5.5: DoubleAngle Identities
 Chapter 5.6: HalfAngle Identities
 Chapter 6: Review Exercises
 Chapter 6.1: Inverse Circular Functions
 Chapter 6.1  6.3: Quiz
 Chapter 6.2: Trigonometric Equations I
 Chapter 6.3: Trigonometric Equations II
 Chapter 6.4: Equations Involving Inverse Trigonometric Functions
 Chapter 7: Summary Exercises on Applications of Trigonometry and Vectors
 Chapter 7.1: Oblique Triangles and the Law of Sines
 Chapter 7.1  7.3: Quiz
 Chapter 7.2: The Ambiguous Case of the Law of Sines
 Chapter 7.3: The Law of Cosines
 Chapter 7.4: Vectors, Operations, and the Dot Product
 Chapter 7.5: Applications of Vectors
 Chapter 8: Review Exercises
 Chapter 8.1: Complex Numbers
 Chapter 8.1  8.4: Quiz
 Chapter 8.2: Trigonometric (Polar) Form of Complex Numbers
 Chapter 8.3: The Product and Quotient Theorems
 Chapter 8.4: De Moivres Theorem; Powers and Roots of Complex Numbers
 Chapter 8.5: Polar Equations and Graphs
 Chapter 8.6: Parametric Equations, Graphs, and Applications
 Chapter Appendix A: Appendix A Exercises
 Chapter Appendix B: Appendix B Exercises
 Chapter Appendix C: Appendix C Exercises
 Chapter Appendix D: Appendix D Exercises
Trigonometry 10th Edition  Solutions by Chapter
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Trigonometry  10th Edition  Solutions by Chapter
Get Full SolutionsThe full stepbystep solution to problem in Trigonometry were answered by Patricia, our top Math solution expert on 01/11/18, 01:35PM. This expansive textbook survival guide covers the following chapters: 59. Trigonometry was written by Patricia and is associated to the ISBN: 9780321671776. Since problems from 59 chapters in Trigonometry have been answered, more than 14746 students have viewed full stepbystep answer. This textbook survival guide was created for the textbook: Trigonometry, edition: 10.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.
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