 145.1: sin 75
 145.2: sin 165
 145.3: cos 255
 145.4: cos (30)
 145.5: sin (240)
 145.6: cos (120)
 145.7: GEOMETRY Determine the exact value of tan in the figure.
 145.8: cos (270  ) = sin
 145.9: sin ( + _ 2 )= cos
 145.10: sin ( + 30) + cos ( + 60) = cos
 145.11: sin 135
 145.12: cos 105
 145.13: sin 285
 145.14: cos 165
 145.15: cos 195
 145.16: sin 255
 145.17: cos 225
 145.18: sin 315
 145.19: sin (15)
 145.20: cos (45)
 145.21: cos (150)
 145.22: sin (165)
 145.23: Salem, OR (Latitude: 44.9 N)
 145.24: Chicago, IL (Latitude: 41.8 N)
 145.25: Charleston, SC (Latitude: 28.5 N)
 145.26: San Diego, CA (Latitude 32.7 N)
 145.27: sin (270  ) = cos
 145.28: cos (90 + ) = sin
 145.29: cos (90  ) = sin
 145.30: sin (90  ) = cos
 145.31: sin ( + _3 2 ) = cos
 145.32: cos (  ) = cos
 145.33: cos (2 + ) = cos
 145.34: sin (  ) = sin
 145.35: Draw a graph of the waves when they are combined.
 145.36: Refer to the application at the beginning of the lesson. What type ...
 145.37: sin (60 + ) + sin (60  )= 3 cos
 145.38: sin ( + _ 3 )  cos ( + _ 6 )= sin
 145.39: sin ( + ) sin (  ) = sin2  sin2 4
 145.40: cos ( + ) = __1  tan tan sec sec
 145.41: OPEN ENDED Give a counterexample to the statement that sin ( + ) = ...
 145.42: REASONING Determine whether cos (  ) < 1 is sometimes, always, or ...
 145.43: CHALLENGE Use the sum and difference formulas for sine and cosine t...
 145.44: Writing in Math Use the information on page 848 to explain how the ...
 145.45: ACT/SAT Find the exact value of sin . A _ 3 2 B _ 2 2 C _1 2 D _ 3 ...
 145.46: REVIEW Refer to the figure below. Which equation could be used to f...
 145.47: cot sec cos2 __ + sin sin cos 4
 145.48: sin2 tan2 (1 cos2 ) sec2 _ csc2 49
 145.49: sin (sin csc ) 2 cos2 50
 145.50: sec tan csc
 145.51: tan csc sec 5
 145.52: 4(sec2 sin2 _ cos2 )
 145.53: (cot tan )sin 5
 145.54: 4(sec2 sin2 _ cos2 )
 145.55: AVIATION A pilot is flying from Chicago to Columbus, a distance of ...
 145.56: Write 6y2 34x2 204 in standard form. (
 145.57: x2 _20 16 5
 145.58: x2 _9 25 5
 145.59: x2 _5 25 6
 145.60: x2 _18 32
Solutions for Chapter 145: Sum and Differences of Angles Formulas
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 145: Sum and Differences of Angles Formulas
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 145: Sum and Differences of Angles Formulas have been answered, more than 55967 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. Chapter 145: Sum and Differences of Angles Formulas includes 60 full stepbystep solutions. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

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.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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.

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

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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).

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

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.