 6.1.1: ________ means measurement of triangles.
 6.1.2: An ________ is determined by rotating a ray about its endpoint.
 6.1.3: Two angles that have the same initial and terminal sides are ________.
 6.1.4: The angle measure that is equivalent to of a complete revolution ab...
 6.1.5: Angles with measures between and are ________ angles, and angles wi...
 6.1.6: Two positive angles that have a sum of are ________ angles, whereas...
 6.1.7: One ________ is the measure of a central angle that intercepts an a...
 6.1.8: The ________ speed of a particle is the ratio of the arc length tra...
 6.1.9: The ________ speed of a particle is the ratio of the change in the ...
 6.1.10: The area of a sector of a circle with radius and central angle wher...
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 6.1.34: (a) 0.355 (b)
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 6.1.50: (a) 6.02 (b) 2.25
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 6.1.71: 45
 6.1.72: 87.4
 6.1.73: 216.35
 6.1.74: 48.27
 6.1.75: 532
 6.1.76: 345
 6.1.77: 0.83
 6.1.78: 0.54
 6.1.79: 7
 6.1.80: 5 11
 6.1.81: 15 8
 6.1.82: 13 2
 6.1.83: 2
 6.1.84: 0.57 1
 6.1.85: 5
 6.1.86: 10 29
 6.1.87: 32
 6.1.88: 75 60
 6.1.89: 4 inches 18 inches
 6.1.90: 14 feet 8 feet
 6.1.91: 14.5 centimeters 25 centimeters
 6.1.92: 80 kilometers 160 kilometers
 6.1.93: 15 inches
 6.1.94: 9 feet
 6.1.95: 3 meters
 6.1.96: 20 centimeters
 6.1.97: 6 inches
 6.1.98: 12 millimeters
 6.1.99: 2.5 feet
 6.1.100: 1.4 miles
 6.1.101: Dallas, Texas Omaha, Nebraska
 6.1.102: San Francisco, California Seattle, Washington
 6.1.103: DIFFERENCE IN LATITUDES Assuming that Earth is a sphere of radius 6...
 6.1.104: DIFFERENCE IN LATITUDES Assuming that Earth is a sphere of radius 6...
 6.1.105: INSTRUMENTATION The pointer on a voltmeter is 6 centimeters in leng...
 6.1.106: ELECTRIC HOIST An electric hoist is being used to lift a beam (see ...
 6.1.107: ANGULAR SPEED A car is moving at a rate of 65 miles per hour, and t...
 6.1.108: ANGULAR SPEED A twoinchdiameter pulley on an electric motor that ...
 6.1.109: LINEAR AND ANGULAR SPEED A inch circular power saw blade rotates a...
 6.1.110: LINEAR AND ANGULAR SPEED A carousel with a 50foot diameter makes 4...
 6.1.111: LINEAR AND ANGULAR SPEED The diameter of a DVD is approximately 12 ...
 6.1.112: ANGULAR SPEED A computerized spin balance machine rotates a 25inch...
 6.1.113: AREA A sprinkler on a golf green is set to spray water over a dista...
 6.1.114: AREA A cars rear windshield wiper rotates The total length of the w...
 6.1.115: AREA A sprinkler system on a farm is set to spray water over a dist...
 6.1.116: SPEED OF A BICYCLE The radii of the pedal sprocket, the wheel sproc...
 6.1.117: A measurement of 4 radians corresponds to two complete revolutions ...
 6.1.118: The difference between the measures of two coterminal angles is alw...
 6.1.119: An angle that measures lies in Quadrant III.
 6.1.120: CAPSTONE Write a short paragraph in your own words explaining the m...
 6.1.121: THINK ABOUT IT A fan motor turns at a given angular speed. How does...
 6.1.122: THINK ABOUT IT Is a degree or a radian the larger unit of measure? ...
 6.1.123: WRITING If the radius of a circle is increasing and the magnitude o...
 6.1.124: PROOF Prove that the area of a circular sector of radius with centr...
Solutions for Chapter 6.1: Angles and Their Measure
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 6.1: Angles and Their Measure
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. Since 124 problems in chapter 6.1: Angles and Their Measure have been answered, more than 48701 students have viewed full stepbystep solutions from this chapter. 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: 8. Chapter 6.1: Angles and Their Measure includes 124 full stepbystep solutions.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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].

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.

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

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 .

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 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.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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)!

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.