 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 , 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 and is associated to the ISBN: 9780321671776. Since problems from 59 chapters in Trigonometry have been answered, more than 29254 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.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Column space C (A) =
space of all combinations of the columns of A.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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 .

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

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.