 6.1: Graph the inverse sine, cosine, and tangent functions, indicating t...
 6.2: The ranges of the inverse tangent and inverse cotangent functions a...
 6.3: It is true that sin 11p 6 =  12 , and therefore arcsin1  12 2 = 1...
 6.4: For all x, tan1tan1 x2 = x.
 6.5: Give the exact real number value of y. Do not use a calculator. y =...
 6.6: Give the exact real number value of y. Do not use a calculator. y =...
 6.7: Give the exact real number value of y. Do not use a calculator. y =...
 6.8: Give the exact real number value of y. Do not use a calculator. y =...
 6.9: Give the exact real number value of y. Do not use a calculator. y =...
 6.10: Give the exact real number value of y. Do not use a calculator. y =...
 6.11: Give the exact real number value of y. Do not use a calculator. y =...
 6.12: Give the exact real number value of y. Do not use a calculator. y =...
 6.13: Give the exact real number value of y. Do not use a calculator. y =...
 6.14: Give the degree measure of u. Do not use a calculator. u = arccos 1...
 6.15: Give the degree measure of u. Do not use a calculator. u = arcsin a...
 6.16: Give the degree measure of u. Do not use a calculator. u = tan1 0 1
 6.17: Use a calculator to give the degree measure of u to the nearest hun...
 6.18: Use a calculator to give the degree measure of u to the nearest hun...
 6.19: Use a calculator to give the degree measure of u to the nearest hun...
 6.20: Use a calculator to give the degree measure of u to the nearest hun...
 6.21: Use a calculator to give the degree measure of u to the nearest hun...
 6.22: Use a calculator to give the degree measure of u to the nearest hun...
 6.23: Evaluate the following without using a calculator. cos1arccos1122 2
 6.24: Evaluate the following without using a calculator. sin aarcsin a 2...
 6.25: Evaluate the following without using a calculator. arccos acos 3p 4...
 6.26: Evaluate the following without using a calculator. arcsec1sec p2 2
 6.27: Evaluate the following without using a calculator. tan1 atan p 4 b 2
 6.28: Evaluate the following without using a calculator. cos11cos 02 2
 6.29: Evaluate the following without using a calculator. sin aarccos 3 4 b 3
 6.30: Evaluate the following without using a calculator. cos1arctan 32 3
 6.31: Evaluate the following without using a calculator. cos1csc11222 3
 6.32: Evaluate the following without using a calculator. sec a2 sin1 a ...
 6.33: Evaluate the following without using a calculator. tan aarcsin 3 5 ...
 6.34: Write each of the following as an algebraic (nontrigonometric) expr...
 6.35: Write each of the following as an algebraic (nontrigonometric) expr...
 6.36: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.37: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.38: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.39: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.40: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.41: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.42: Give all exact solutions, in radians, for each equation sec x 2 = c...
 6.43: Give all exact solutions, in radians, for each equation cos 2x + co...
 6.44: Give all exact solutions, in radians, for each equation 4 sin x cos...
 6.45: Solve each equation for exact solutions over the interval 30, 3602 ...
 6.46: Solve each equation for exact solutions over the interval 30, 3602 ...
 6.47: Solve each equation for exact solutions over the interval 30, 3602 ...
 6.48: Solve each equation for exact solutions over the interval 30, 3602 ...
 6.49: Solve each equation for exact solutions over the interval 30, 3602 ...
 6.50: Solve each equation for exact solutions over the interval 30, 3602 ...
 6.51: Give all exact solutions, in degrees, for each equation. 223 cos u ...
 6.52: Give all exact solutions, in degrees, for each equation. sin u  co...
 6.53: Give all exact solutions, in degrees, for each equation. tan u  se...
 6.54: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.55: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.56: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.57: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.58: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.59: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.60: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.61: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.62: Solve each equation for x. In Exercises 5861, x is restricted to th...
 6.63: Viewing Angle of an Observer A 10ftwide chalkboard is situated 5 ...
 6.64: Snells Law Recall Snells law from Exercises 69 and 70 of Section 2....
 6.65: Snells Law Refer to Exercise 64. What happens when u1 is greater th...
 6.66: British Nautical Mile The British nautical mile is defined as the l...
 6.67: The function y = csc1 x is not found on graphing calculators. Howe...
 6.68: (a) Use the graph of y = sin1 x to approximate sin1 0.4. (b) Use ...
Solutions for Chapter 6: Review Exercises
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 6: Review Exercises
Get Full SolutionsThis textbook survival guide was created for the textbook: Trigonometry, edition: 10. Since 68 problems in chapter 6: Review Exercises have been answered, more than 35429 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Trigonometry was written by and is associated to the ISBN: 9780321671776. Chapter 6: Review Exercises includes 68 full stepbystep solutions.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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.

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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.

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

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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

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.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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).

Solvable system Ax = b.
The right side b is in the column space of A.

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.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

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