 106.1: Mia said that if you know the sine value of each acute angle,then y...
 106.2: If sin A 5 ,is cos A 5 always true? Explain why or why not.
 106.3: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.4: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.5: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.6: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.7: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.8: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.9: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.10: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.11: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.12: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.13: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.14: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.15: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.16: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.17: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.18: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.19: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.20: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.21: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.22: In 322:a. Rewrite each function value in terms of its cofunction.b....
 106.23: If sin u5cos (20 1u),what is the value of u?
 106.24: For what value of x does tan (x 1 10) 5 cot (40 1 x)?
 106.25: Complete the following table of cofunctions for radian values.
 106.26: In 2633: a. Rewrite each function value in terms of its cofunction....
 106.27: In 2633: a. Rewrite each function value in terms of its cofunction....
 106.28: In 2633: a. Rewrite each function value in terms of its cofunction....
 106.29: In 2633: a. Rewrite each function value in terms of its cofunction....
 106.30: In 2633: a. Rewrite each function value in terms of its cofunction....
 106.31: In 2633: a. Rewrite each function value in terms of its cofunction....
 106.32: In 2633: a. Rewrite each function value in terms of its cofunction....
 106.33: In 2633: a. Rewrite each function value in terms of its cofunction....
Solutions for Chapter 106: COFUNCTIONS
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 106: COFUNCTIONS
Get Full SolutionsAmsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. Since 33 problems in chapter 106: COFUNCTIONS have been answered, more than 30661 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 106: COFUNCTIONS includes 33 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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.

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

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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

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

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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

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