 118.1: Calvin said that the graph of y 5 tan has asymptotes at x 5 1 np fo...
 118.2: Is the graph of y 5 sin the graph of y 5 sin 2x moved units to the ...
 118.3: In 314, sketch one cycle of the graph. y 5 2 sin x
 118.4: In 314, sketch one cycle of the graph. y 5 3 sin 2x
 118.5: In 314, sketch one cycle of the graph. y 5 cos 3x
 118.6: In 314, sketch one cycle of the graph. y 5 2 sin x
 118.7: In 314, sketch one cycle of the graph. y 5 4 cos 2x
 118.8: In 314, sketch one cycle of the graph. y 5 3 sin
 118.9: In 314, sketch one cycle of the graph. y 5 cos
 118.10: In 314, sketch one cycle of the graph. y 5 4 sin (x 2 p)
 118.11: In 314, sketch one cycle of the graph. y 5 tan x
 118.12: In 314, sketch one cycle of the graph. . y 5 tan
 118.13: In 314, sketch one cycle of the graph. y 5 22 sin x
 118.14: In 314, sketch one cycle of the graph. y 5 2cos x
 118.15: In 1520, for each of the following, write the equation of the graph...
 118.16: In 1520, for each of the following, write the equation of the graph...
 118.17: In 1520, for each of the following, write the equation of the graph...
 118.18: In 1520, for each of the following, write the equation of the graph...
 118.19: In 1520, for each of the following, write the equation of the graph...
 118.20: In 1520, for each of the following, write the equation of the graph...
 118.21: a. On the same set of axes, sketch the graphs of y 5 2 sin x and y ...
 118.22: a. On the same set of axes, sketch the graphs of y 5 tan x and y 5 ...
 118.23: a. On the same set of axes, sketch the graphs of y 5 sin 3x and y 5...
Solutions for Chapter 118: SKETCHING TRIGONOMETRIC GRAPHS
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 118: SKETCHING TRIGONOMETRIC GRAPHS
Get Full SolutionsChapter 118: SKETCHING TRIGONOMETRIC GRAPHS includes 23 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Since 23 problems in chapter 118: SKETCHING TRIGONOMETRIC GRAPHS have been answered, more than 29483 students have viewed full stepbystep solutions from this chapter. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This expansive textbook survival guide covers the following chapters and their solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Iterative method.
A sequence of steps intended to approach the desired solution.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

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

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 •

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.