 8.2.1: What isthe domain and the range ofy = sec x?
 8.2.2: True or False The graph of y = sec x is onetoone on the interval ...
 8.2.3: If tan u = then sin u = 12,  p26 u 6 p2
 8.2.4: y = sec x 1 x means , where y , y Z p 2
 8.2.5: To find the inverse secant of a real number x such that x 1, conver...
 8.2.6: True or False It is impossible to obtain exact values for the inver...
 8.2.7: True or False csc1 0.5 is not defined
 8.2.8: True or False The domain of the inverse cotangent function is the s...
 8.2.9: In 936, find the exact value of each expressioncosasin b 1 22 2 b
 8.2.10: In 936, find the exact value of each expressionsinacos b d 1 1 2
 8.2.11: In 936, find the exact value of each expressiontanccos b d 1 a 23...
 8.2.12: In 936, find the exact value of each expressionancsin1 a 1 2 tanc...
 8.2.13: In 936, find the exact value of each expressionsecacos b d 1 1 2
 8.2.14: In 936, find the exact value of each expressioncotcsin 12 1 a 1 2
 8.2.15: In 936, find the exact value of each expressioncsc1tan 1 23B 1 co...
 8.2.16: In 936, find the exact value of each expressionsecAtan csc1tan 1 23
 8.2.17: In 936, find the exact value of each expressionsin3tan b d 1 1124
 8.2.18: In 936, find the exact value of each expressioncoscsin b d 1 a 23...
 8.2.19: In 936, find the exact value of each expressioneccsin b d 1 a 1 2...
 8.2.20: In 936, find the exact value of each expressioncscccos1 a 23 2 se...
 8.2.21: In 936, find the exact value of each expressioncos b 1 asin 5p 4
 8.2.22: In 936, find the exact value of each expressiontan b d 1 acot 2p 3
 8.2.23: In 936, find the exact value of each expressionsin b d 1 ccosa 7p 6
 8.2.24: In 936, find the exact value of each expressioncos1 ctana p 4 sin b
 8.2.25: In 936, find the exact value of each expressiontanasin1 b 1 3
 8.2.26: In 936, find the exact value of each expressiontanacos b 1 1 3
 8.2.27: In 936, find the exact value of each expressionsecatan b 1 1 2 tan...
 8.2.28: In 936, find the exact value of each expressioncosasin1 22 3
 8.2.29: In 936, find the exact value of each expressioncotcsin 1224 1 a ...
 8.2.30: In 936, find the exact value of each expressioncsc3tan 1324 1 cot...
 8.2.31: In 936, find the exact value of each expressionsin3tan b d 1 csc3t...
 8.2.32: In 936, find the exact value of each expressioncotccos1 a 23 3 si...
 8.2.33: In 936, find the exact value of each expressionsecasin1 b 225 5
 8.2.34: In 936, find the exact value of each expressioncscatan b 1 1 2
 8.2.35: In 936, find the exact value of each expressionin b 1 acos 3p 4
 8.2.36: In 936, find the exact value of each expressioncos1 asin 7p 6
 8.2.37: In 3744, find the exact value of each expression.
 8.2.38: In 3744, find the exact value of each expression.
 8.2.39: In 3744, find the exact value of each expression.
 8.2.40: In 3744, find the exact value of each expression.
 8.2.41: In 3744, find the exact value of each expression.
 8.2.42: In 3744, find the exact value of each expression.
 8.2.43: In 3744, find the exact value of each expression.
 8.2.44: In 3744, find the exact value of each expression.
 8.2.45: In 4556, use a calculator to find the value of each expression roun...
 8.2.46: In 4556, use a calculator to find the value of each expression roun...
 8.2.47: In 4556, use a calculator to find the value of each expression roun...
 8.2.48: In 4556, use a calculator to find the value of each expression roun...
 8.2.49: In 4556, use a calculator to find the value of each expression roun...
 8.2.50: In 4556, use a calculator to find the value of each expression roun...
 8.2.51: In 4556, use a calculator to find the value of each expression roun...
 8.2.52: In 4556, use a calculator to find the value of each expression roun...
 8.2.53: In 4556, use a calculator to find the value of each expression roun...
 8.2.54: In 4556, use a calculator to find the value of each expression roun...
 8.2.55: In 4556, use a calculator to find the value of each expression roun...
 8.2.56: In 4556, use a calculator to find the value of each expression roun...
 8.2.57: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.58: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.59: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.60: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.61: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.62: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.63: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.64: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.65: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.66: In 5766, write each trigonometric expression as an algebraic expres...
 8.2.67: In 6778, , , and Find the exact value of each composite function.
 8.2.68: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.69: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.70: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.71: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.72: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.73: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.74: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.75: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.76: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.77: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.78: In 6778, f1x2 = sin x,  g1x2 = cos x, 0 x p . p2 x p2 , , and h1x2...
 8.2.79: 79 and 80 require the following discussion:When granular materials ...
 8.2.80: 79 and 80 require the following discussion:When granular materials ...
 8.2.81: Artillery A projectile fired into the first quadrant from the origi...
 8.2.82: Using a graphing utility, graphy = cot1 x
 8.2.83: Using a graphing utility, graphy = sec1 x
 8.2.84: Using a graphing utility, graphy = csc1 x.
 8.2.85: Explain in your own words how you would use your calculator to find...
 8.2.86: Consult three books on calculus and write down the definition in ea...
Solutions for Chapter 8.2: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 8.2
Get Full SolutionsSince 86 problems in chapter 8.2 have been answered, more than 57688 students have viewed full stepbystep solutions from this chapter. Chapter 8.2 includes 86 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9.

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!

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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.

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

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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 .

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.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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

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.

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

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}.

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.