 114.1: Tyler said that one cycle of a cosine curve has a maximum value at ...
 114.2: Is the graph of y 5 sin 2(x 1 p) the same as the graph of y 5 sin 2...
 114.3: In 314, for each of the following, write the equation of the graph ...
 114.4: In 314, for each of the following, write the equation of the graph ...
 114.5: In 314, for each of the following, write the equation of the graph ...
 114.6: In 314, for each of the following, write the equation of the graph ...
 114.7: In 314, for each of the following, write the equation of the graph ...
 114.8: In 314, for each of the following, write the equation of the graph ...
 114.9: In 314, for each of the following, write the equation of the graph ...
 114.10: In 314, for each of the following, write the equation of the graph ...
 114.11: In 314, for each of the following, write the equation of the graph ...
 114.12: In 314, for each of the following, write the equation of the graph ...
 114.13: In 314, for each of the following, write the equation of the graph ...
 114.14: In 314, for each of the following, write the equation of the graph ...
 114.15: Motion that can be described by a sine or cosine function is called...
Solutions for Chapter 114: Graphs of Trigonometric Functions
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 114: Graphs of Trigonometric Functions
Get Full SolutionsSince 15 problems in chapter 114: Graphs of Trigonometric Functions have been answered, more than 28472 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. Chapter 114: Graphs of Trigonometric Functions includes 15 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1.

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

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

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.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·