 Chapter 14.1: sin 135
 Chapter 14.2: tan 315
 Chapter 14.3: cos 90
 Chapter 14.4: tan 45
 Chapter 14.5: sin _5 4
 Chapter 14.6: cos _7 6
 Chapter 14.7: cos (150)
 Chapter 14.8: cot _9 4
 Chapter 14.9: sec _13 6
 Chapter 14.10: tan ( _3 2 ) 1
 Chapter 14.11: tan _8 3
 Chapter 14.12: csc (720)
 Chapter 14.13: AMUSEMENT The distance from the highest point of a Ferris wheel to ...
 Chapter 14.14: 15x2  5x
 Chapter 14.15: 2x4  4x2
 Chapter 14.16: x3 +
 Chapter 14.17: 2x2  3x  2
 Chapter 14.18: PARKS The rectangular wooded area of a park covers x2  6x + 8 squa...
 Chapter 14.19: x2  5x  24 = 0
 Chapter 14.20: x2  2x  48 = 0
 Chapter 14.21: x2  12x = 0
 Chapter 14.22: x2  16 = 0
 Chapter 14.23: HOME IMPROVEMENT You are putting new flooring in your laundry room,...
 Chapter 14.24: sin csc  cos2
 Chapter 14.25: cos2 sec csc
 Chapter 14.26: cos + sin tan
 Chapter 14.27: sin (1 + cot2 )
 Chapter 14.28: PHYSICS The magnetic force on a particle can be modeled by the equa...
 Chapter 14.29: sin tan + _cos cot = cos + sin
 Chapter 14.30: sin 1  cos = csc + cot
 Chapter 14.31: cot2 sec2 = 1 + cot2
 Chapter 14.32: sec ( sec  cos ) = tan2
 Chapter 14.33: OPTICS The amount of light passing through a polarization filter ca...
 Chapter 14.34: cos 15
 Chapter 14.35: cos 285
 Chapter 14.36: sin 150
 Chapter 14.37: sin 195
 Chapter 14.38: cos (210)
 Chapter 14.39: sin (105)
 Chapter 14.40: cos (90 + ) = sin
 Chapter 14.41: sin (30 ) = cos (60 + )
 Chapter 14.42: sin ( + ) = sin
 Chapter 14.43: cos = (cos + )
 Chapter 14.44: sin = _1 4 ; 0 < < 90
 Chapter 14.45: sin = _5 13; 180 < < 270
 Chapter 14.46: cos = _5 17 ; 90 < < 180
 Chapter 14.47: cos = _12 13; 270 < < 360
 Chapter 14.48: 2 sin 2 = 1
 Chapter 14.49: cos2 + sin2 = 2 cos 0
 Chapter 14.50: PRISMS The horizontal and vertical components of an oblique prism c...
Solutions for Chapter Chapter 14: Trigonometric Graphs and Identities
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter Chapter 14: Trigonometric Graphs and Identities
Get Full SolutionsChapter Chapter 14: Trigonometric Graphs and Identities includes 50 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. Since 50 problems in chapter Chapter 14: Trigonometric Graphs and Identities have been answered, more than 52450 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1.

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

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.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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.

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.

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 .

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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 matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Outer product uv T
= column times row = rank one matrix.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

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.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).