 6.1: In Exercises 1 to 10, find the exact value.
 6.2: In Exercises 1 to 10, find the exact value.
 6.3: In Exercises 1 to 10, find the exact value.
 6.4: In Exercises 1 to 10, find the exact value.
 6.5: In Exercises 1 to 10, find the exact value.
 6.6: In Exercises 1 to 10, find the exact value.
 6.7: In Exercises 1 to 10, find the exact value.
 6.8: In Exercises 1 to 10, find the exact value.
 6.9: In Exercises 1 to 10, find the exact value.
 6.10: In Exercises 1 to 10, find the exact value.
 6.11: In Exercises 11 to 14, find the exact value of the given function.
 6.12: In Exercises 11 to 14, find the exact value of the given function.
 6.13: In Exercises 11 to 14, find the exact value of the given function.
 6.14: In Exercises 11 to 14, find the exact value of the given function.
 6.15: In Exercises 15 to 18, use a cofunction identity to write an equiva...
 6.16: In Exercises 15 to 18, use a cofunction identity to write an equiva...
 6.17: In Exercises 15 to 18, use a cofunction identity to write an equiva...
 6.18: In Exercises 15 to 18, use a cofunction identity to write an equiva...
 6.19: In Exercises 19 to 24, write the given expression as a single trigo...
 6.20: In Exercises 19 to 24, write the given expression as a single trigo...
 6.21: In Exercises 19 to 24, write the given expression as a single trigo...
 6.22: In Exercises 19 to 24, write the given expression as a single trigo...
 6.23: In Exercises 19 to 24, write the given expression as a single trigo...
 6.24: In Exercises 19 to 24, write the given expression as a single trigo...
 6.25: In Exercises 25 and 26, use powerreducing identities to verify eac...
 6.26: In Exercises 25 and 26, use powerreducing identities to verify eac...
 6.27: In Exercises 27 and 28, use a producttosum identity to verify eac...
 6.28: In Exercises 27 and 28, use a producttosum identity to verify eac...
 6.29: In Exercises 29 to 32, write each expression as the product of two ...
 6.30: In Exercises 29 to 32, write each expression as the product of two ...
 6.31: In Exercises 29 to 32, write each expression as the product of two ...
 6.32: In Exercises 29 to 32, write each expression as the product of two ...
 6.33: In Exercises 33 to 50, verify the identity
 6.34: In Exercises 33 to 50, verify the identity
 6.35: In Exercises 33 to 50, verify the identity
 6.36: In Exercises 33 to 50, verify the identity
 6.37: In Exercises 33 to 50, verify the identity
 6.38: In Exercises 33 to 50, verify the identity
 6.39: In Exercises 33 to 50, verify the identity
 6.40: In Exercises 33 to 50, verify the identity
 6.41: In Exercises 33 to 50, verify the identity
 6.42: In Exercises 33 to 50, verify the identity
 6.43: In Exercises 33 to 50, verify the identity
 6.44: In Exercises 33 to 50, verify the identity
 6.45: In Exercises 33 to 50, verify the identity
 6.46: In Exercises 33 to 50, verify the identity
 6.47: In Exercises 33 to 50, verify the identity
 6.48: In Exercises 33 to 50, verify the identity
 6.49: In Exercises 33 to 50, verify the identity
 6.50: In Exercises 33 to 50, verify the identity
 6.51: In Exercises 51 to 54, evaluate each expression.
 6.52: In Exercises 51 to 54, evaluate each expression.
 6.53: In Exercises 51 to 54, evaluate each expression.
 6.54: In Exercises 51 to 54, evaluate each expression.
 6.55: In Exercises 55 and 56, solve each equation.
 6.56: In Exercises 55 and 56, solve each equation.
 6.57: In Exercises 57 and 58, find all solutions of each equation with .
 6.58: In Exercises 57 and 58, find all solutions of each equation with .
 6.59: In Exercises 59 and 60, solve the trigonometric equation where x is...
 6.60: In Exercises 59 and 60, solve the trigonometric equation where x is...
 6.61: In Exercises 61 and 62, solve each equation on
 6.62: In Exercises 61 and 62, solve each equation on
 6.63: In Exercises 63 to 66, write the equation in the form where the mea...
 6.64: In Exercises 63 to 66, write the equation in the form where the mea...
 6.65: In Exercises 63 to 66, write the equation in the form where the mea...
 6.66: In Exercises 63 to 66, write the equation in the form where the mea...
 6.67: In Exercises 67 and 68, find the exact value of each composition of...
 6.68: In Exercises 67 and 68, find the exact value of each composition of...
 6.69: In Exercises 69 to 72, graph each function.
 6.70: In Exercises 69 to 72, graph each function.
 6.71: In Exercises 69 to 72, graph each function.
 6.72: In Exercises 69 to 72, graph each function.
 6.73: Sunrise Time The following table shows the sunrise time for Tampa, ...
Solutions for Chapter 6: College Algebra and Trigonometry 7th Edition
Full solutions for College Algebra and Trigonometry  7th Edition
ISBN: 9781439048603
Solutions for Chapter 6
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048603. Chapter 6 includes 73 full stepbystep solutions. Since 73 problems in chapter 6 have been answered, more than 5948 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra and Trigonometry, edition: 7.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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.

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

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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).

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

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.

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

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)!

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

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.