 132.1: 70
 132.2: 300
 132.3: 570
 132.4: 45
 132.5: 130
 132.6: 10
 132.7: 485
 132.8: 3 4
 132.9:  _ 6
 132.10: 19 3
 132.11: How long does it take Earth to rotate through an angle of 315?
 132.12: How long does it take Earth to rotate through an angle of _ 6 ?
 132.13: 60
 132.14: 425
 132.15: 3
 132.16: 235
 132.17: 270
 132.18: 790
 132.19: 380
 132.20: 120
 132.21: 60
 132.22: 15
 132.23: 225
 132.24: 5 6
 132.25: 11 4
 132.26:  _ 4
 132.27:  _ 3
 132.28: 225
 132.29: 30
 132.30: 15
 132.31: 3 4
 132.32: 7 6
 132.33:  _5 4
 132.34: Find the area of a sector with a central angle of 4_ 3 radians in a...
 132.35: Find the area of a sector with a central angle of 150 in a circle w...
 132.36: 150
 132.37: 50
 132.39:  _2 3
 132.40: 660
 132.41: 570
 132.42: 158
 132.43: 260
 132.44: 29 4
 132.45: 17 6
 132.46: 9
 132.47: 3
 132.48: 140
 132.49: 368
 132.50: 760
 132.51:  _2 3
 132.52: 9 2
 132.53: 17 4
 132.54: DRIVING Some sportutility vehicles (SUVs) use 15inch radius wheel...
 132.55: ENTERTAINMENT Suppose the gondolas on the Navy Pier Ferris Wheel we...
 132.56: CARS Use the Area of a Sector Formula in Exercises 34 and 35 to fin...
 132.57: OPEN ENDED Draw and label an example of an angle with negative meas...
 132.58: CHALLENGE A line with positive slope makes an angle of _ 2 radians ...
 132.59: CHALLENGE If (a, b) is on a circle that has radius r and center at ...
 132.60: REASONING Express _1 8 of a revolution in degrees.
 132.61: REASONING Express _1 8 of a revolution in degrees.
 132.62: ACT/SAT Choose the radian measure that is equal to 56. A _ 15 B _7 ...
 132.63: REVIEW Angular velocity is defined by the equation = _ t , where is...
 132.64: A = 34, b = 5
 132.65: B = 68, b = 14.7
 132.66: B = 55, c = 16 6
 132.67: a = 0.4, b = 0.4 3
 132.68: p = 72%, n = 100
 132.69: p = 50%, n = 200
 132.70: choosing an arrangement of 5 CDs from your 30 favorite CDs
 132.71: choosing 3 different types of snack foods out of 7 at the store to ...
 132.72: g(x) = 2x h(x) = 3x  4 h
 132.73: g(x) = 2x + 5 h(x) = 2x2  3x + 9
 132.74: 2 3
 132.75: 3 5
 132.76: 4 6
 132.77: 5 10
 132.78: 7 2
 132.79: 5 8 6
Solutions for Chapter 132: Angles and Angle Measure
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 132: Angles and Angle Measure
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Since 78 problems in chapter 132: Angles and Angle Measure have been answered, more than 60684 students have viewed full stepbystep solutions from this chapter. Chapter 132: Angles and Angle Measure includes 78 full stepbystep solutions.

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.

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

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

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

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).

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

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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).

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

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.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.