 1.3.1: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.2: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.3: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.4: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.5: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.6: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.7: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.8: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.9: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.10: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.11: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.12: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.13: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.14: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.15: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.16: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.17: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.18: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.19: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.20: Concept Check Sketch an angle u in standard position such that u ha...
 1.3.21: For any nonquadrantal angle u, sin u and csc u will have the same s...
 1.3.22: Concept Check How is the value of r interpreted geometrically in th...
 1.3.23: Concept Check If cot u is undefined, what is the value of tan u?
 1.3.24: Concept Check If the terminal side of an angle u is in quadrant III...
 1.3.25: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.26: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.27: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.28: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.29: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.30: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.31: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.32: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.33: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.34: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.35: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.36: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.37: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.38: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.39: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.40: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.41: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.42: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.43: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.44: Concept Check Suppose that the point 1x, y2 is in the indicated qua...
 1.3.45: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.46: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.47: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.48: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.49: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.50: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.51: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.52: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.53: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.54: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.55: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.56: In Exercises 4556, an equation of the terminal side of an angle u i...
 1.3.57: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.58: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.59: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.60: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.61: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.62: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.63: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.64: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.65: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.66: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.67: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.68: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.69: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.70: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.71: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.72: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.73: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.74: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.75: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.76: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.77: To work Exercises 5777, begin by reproducing the graph in Figure 29...
 1.3.78: Explain how the answer to Exercise 77 can be given once the answers...
 1.3.79: Use the trigonometric function values of quadrantal angles given in...
 1.3.80: Use the trigonometric function values of quadrantal angles given in...
 1.3.81: Use the trigonometric function values of quadrantal angles given in...
 1.3.82: Use the trigonometric function values of quadrantal angles given in...
 1.3.83: Use the trigonometric function values of quadrantal angles given in...
 1.3.84: Use the trigonometric function values of quadrantal angles given in...
 1.3.85: Use the trigonometric function values of quadrantal angles given in...
 1.3.86: Use the trigonometric function values of quadrantal angles given in...
 1.3.87: Use the trigonometric function values of quadrantal angles given in...
 1.3.88: Use the trigonometric function values of quadrantal angles given in...
 1.3.89: Use the trigonometric function values of quadrantal angles given in...
 1.3.90: Use the trigonometric function values of quadrantal angles given in...
 1.3.91: Use the trigonometric function values of quadrantal angles given in...
 1.3.92: Use the trigonometric function values of quadrantal angles given in...
 1.3.93: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.94: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.95: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.96: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.97: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.98: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.99: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.100: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.101: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.102: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.103: The angles 15 and 75 are complementary. With your calculator determ...
 1.3.104: The angles 25 and 65 are complementary. With your calculator determ...
 1.3.105: With your calculator determine sin 10 and sin1102. Make a conjectu...
 1.3.106: With your calculator determine cos 20 and cos1202. Make a conjectu...
 1.3.107: In Exercises 107112, set your TI graphing calculator in parametric ...
 1.3.108: In Exercises 107112, set your TI graphing calculator in parametric ...
 1.3.109: In Exercises 107112, set your TI graphing calculator in parametric ...
 1.3.110: In Exercises 107112, set your TI graphing calculator in parametric ...
 1.3.111: In Exercises 107112, set your TI graphing calculator in parametric ...
 1.3.112: In Exercises 107112, set your TI graphing calculator in parametric ...
Solutions for Chapter 1.3: Trigonometric Functions
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 1.3: Trigonometric Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 112 problems in chapter 1.3: Trigonometric Functions have been answered, more than 32925 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780321671776. This textbook survival guide was created for the textbook: Trigonometry, edition: 10. Chapter 1.3: Trigonometric Functions includes 112 full stepbystep solutions.

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.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

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!

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

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

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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.

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).

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

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).