 122.1: Is sin u 5 an identity? Explain why or why not.
 122.2: Cory said that in Example 3, 1 2 sin u 5 could have been shown to b...
 122.3: In 326, prove that each equation is an identity. sin u csc u cos u ...
 122.4: In 326, prove that each equation is an identity. tan u sin u cos u ...
 122.5: In 326, prove that each equation is an identity. cot u sin u cos u ...
 122.6: In 326, prove that each equation is an identity. sec u (cos u 2 cot...
 122.7: In 326, prove that each equation is an identity. csc u (sin u 1 tan...
 122.8: In 326, prove that each equation is an identity. 1 2 5 sin2 u
 122.9: In 326, prove that each equation is an identity. 1 2 5 cos2 u
 122.10: In 326, prove that each equation is an identity. sin u (csc u 2 sin...
 122.11: In 326, prove that each equation is an identity. cos u (sec u 2 cos...
 122.12: In 326, prove that each equation is an identity. 5 sin u
 122.13: In 326, prove that each equation is an identity. 5 cos u
 122.14: In 326, prove that each equation is an identity. 5 cot u
 122.15: In 326, prove that each equation is an identity. 5 tan u
 122.16: In 326, prove that each equation is an identity. 2 5 tan u
 122.17: In 326, prove that each equation is an identity. 2 5 cot u
 122.18: In 326, prove that each equation is an identity. 5 1 2 cos u
 122.19: In 326, prove that each equation is an identity. 5 1 2 sin u
 122.20: In 326, prove that each equation is an identity. sec u csc u 5 tan ...
 122.21: In 326, prove that each equation is an identity. 2 1 5 sec u
 122.22: In 326, prove that each equation is an identity. cos u1 5 1
 122.23: In 326, prove that each equation is an identity. sin u1 5 1
 122.24: In 326, prove that each equation is an identity. 2 tan2 u 5 1
 122.25: In 326, prove that each equation is an identity. 2 cot2 u 5 1
 122.26: In 326, prove that each equation is an identity. 1 5
 122.27: For what values of u is the identity 1 5 1 undefined?
Solutions for Chapter 122: PROVING AN IDENTITY
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 122: PROVING AN IDENTITY
Get Full SolutionsThis textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. 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 122: PROVING AN IDENTITY includes 27 full stepbystep solutions. Since 27 problems in chapter 122: PROVING AN IDENTITY have been answered, more than 29359 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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

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

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.