 6.1:
 6.2:
 6.3: 85 3
 6.4: 310
 6.5: 110 4
 6.6: 405
 6.7: 15 4
 6.8: 2 9
 6.9: 4 3
 6.10: 23 3 4
 6.11: 450
 6.12: 120
 6.13: 16.5 1
 6.14: 112.5
 6.15: 33 45 9
 6.16: 98 25
 6.17: 84 15
 6.18: 196 77
 6.19: 3 10
 6.20: 7 5
 6.21: 3 5 2007
 6.22: 11 6
 6.23: 3.5 8
 6.24: 8.3
 6.25: 4.75
 6.26: 6
 6.27: ARC LENGTH Find the length of the arc on a circle with a radius of ...
 6.28: BICYCLE At what speed is a bicyclist traveling when his 27inchdia...
 6.29: CIRCULAR SECTOR Find the area of the sector of a circle with a radi...
 6.30: CIRCULAR SECTOR Find the area of the sector of a circle with a radi...
 6.31: 5 4
 6.32: 8 4
 6.33: in 1 3
 6.34: tan 4
 6.35: csc 4
 6.36: csc 5
 6.37: tan 41
 6.38: csc 7
 6.39: cos 38.9 s
 6.40: sec 79.3
 6.41: cot 25 13
 6.42: sin 76 20 51
 6.43: cos 18
 6.44: tan 5 6
 6.45: RAILROAD GRADE A train travels 3.5 kilometers on a straight track w...
 6.46: GUY WIRE A guy wire runs from the ground to the top of a 25foot te...
 6.47:
 6.48:
 6.49:
 6.50:
 6.51: 0.5, 4.5 0
 6.52: 0.2, 0.8
 6.53: x, 4x, x > 0
 6.54: 2x, 3x, x > 0
 6.55: sec tan < 0
 6.56: csc cos < 0
 6.57: tan cos < 0
 6.58: sin cos < 0
 6.59: tan sin > 0 4
 6.60: cos sin > 0 2
 6.61: 264
 6.62: 635
 6.63: 6 5
 6.64: 17 3
 6.65: 3
 6.66: 4
 6.67: 5 6 2005
 6.68: 5 3
 6.69: 7 3 5 4
 6.70: 5 4 2005
 6.71: 495
 6.72: 120
 6.73: 150 4
 6.74: 420
 6.75: sin 10
 6.76: tan 3
 6.77: sec 2.8
 6.78: cos 5.5
 6.79: sin 17 15 ta
 6.80: tan 25 7 s
 6.81: t 2 3 t
 6.82: t 7 4
 6.83: t 7 6 t
 6.84: t 3 4
 6.85: y sin 6x
 6.86: y cos 3x
 6.87: y 3 cos 2x y
 6.88: y 2 sin x
 6.89: f x 5 sin 2x 5
 6.90: f x 8 cos x 4
 6.91: y 5 sin x
 6.92: y 4 cos x f
 6.93: g t
 6.94: g t 3 cos t 5
 6.95: SOUND WAVES Sound waves can be modeled by sine functions of the for...
 6.96: DATA ANALYSIS: METEOROLOGY The times of sunset (Greenwich Mean Time...
 6.97: f x 3 tan 2x
 6.98: f t tant 2 f
 6.99: f x
 6.100: g t 2 cot 2t
 6.101: f x 3 sec x
 6.102: h t sect 4 f
 6.103: f x 1 2 csc x 2
 6.104: f t 3 csc2t 4 f
 6.105: f x x cos x
 6.106: g x ex cos x
 6.107: arcsin
 6.108: arcsin
 6.109: arcsin 0.4
 6.110: arcsin 0.213
 6.111: sin
 6.112: sin1 0.89
 6.113: arccos
 6.114: arccos
 6.115: cos
 6.116: cos1 3 2 1
 6.117: arccos 0.425
 6.118: arccos
 6.119: tan
 6.120: tan
 6.121: f x 2 arcsin x 2
 6.122: f x 3 arccos x
 6.123: f x arctan x 2
 6.124: f x arcsin 2x
 6.125: cos arctan 3 4
 6.126: tan arccos 3 5
 6.127: sec arctan
 6.128: cot arcsin 12
 6.129: tan arccos x 2
 6.130: sec arcsin x 1 c
 6.131: ANGLE OF ELEVATION The height of a radio transmission tower is 70 m...
 6.132: SKI SLOPE A ski slope on a mountain has an angle of elevation of Th...
 6.133: NAVIGATION A ship leaves port at noon and has a bearing of The ship...
 6.134: WAVE MOTION Your fishing bobber oscillates in simple harmonic motio...
 6.135: y sin sin 30 sin 1
 6.136: Because tan
 6.137: WRITING Describe the behavior of at the zeros of Explain your reaso...
 6.138: CONJECTURE (a) Use a graphing utility to complete the table. (b) Ma...
 6.139: WRITING When graphing the sine and cosine functions, determining th...
 6.140: OSCILLATION OF A SPRING A weight is suspended from a ceiling by a s...
 6.141: The base of the triangle shown in the figure is also the radius of ...
Solutions for Chapter 6: Trigonometry
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 6: Trigonometry
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Since 141 problems in chapter 6: Trigonometry have been answered, more than 46754 students have viewed full stepbystep solutions from this chapter. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. Chapter 6: Trigonometry includes 141 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).

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.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Iterative method.
A sequence of steps intended to approach the desired solution.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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

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

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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.

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

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