 6.2.1: In a right triangle, with legs a and b and hypotenuse c, the Pythag...
 6.2.2: The value of the function f1x2 = 3x  7 at 5 is . (pp. 6164)
 6.2.3: For a function y = f1x2, for each x in the domain, there is exactly...
 6.2.4: If two triangles are similar, then corresponding angles are and the...
 6.2.5: What point is symmetric with respect to the yaxis to the point a 1...
 6.2.6: If 1x, y2 is a point on the unit circle in quadrant IV and if x = 2...
 6.2.7: The function takes as input a real number t that corresponds to a p...
 6.2.8: The point on the unit circle that corresponds to u = p 2 is P = .
 6.2.9: The point on the unit circle that corresponds to u = p 4 is P = .
 6.2.10: The point on the unit circle that corresponds to u = p 3 is P = .
 6.2.11: For any angle u in standard position, let P = (x, y) be the point o...
 6.2.12: Exact values can be found for the sine of any angle.
 6.2.13: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.14: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.15: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.16: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.17: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.18: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.19: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.20: In 1320, P = 1x, y2 is the point on the unit circle that correspond...
 6.2.21: In 2130, find the exact value. Do not use a calculator.
 6.2.22: In 2130, find the exact value. Do not use a calculator.
 6.2.23: In 2130, find the exact value. Do not use a calculator.
 6.2.24: In 2130, find the exact value. Do not use a calculator.
 6.2.25: In 2130, find the exact value. Do not use a calculator.
 6.2.26: In 2130, find the exact value. Do not use a calculator.
 6.2.27: In 2130, find the exact value. Do not use a calculator.
 6.2.28: In 2130, find the exact value. Do not use a calculator.
 6.2.29: In 2130, find the exact value. Do not use a calculator.
 6.2.30: In 2130, find the exact value. Do not use a calculator.
 6.2.31: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.32: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.33: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.34: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.35: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.36: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.37: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.38: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.39: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.40: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.41: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.42: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.43: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.44: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.45: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.46: In 3146, find the exact value of each expression. Do not use a calc...
 6.2.47: In 4764, find the exact values of the six trigonometric functions o...
 6.2.48: In 4764, find the exact values of the six trigonometric functions o...
 6.2.49: In 4764, find the exact values of the six trigonometric functions o...
 6.2.50: In 4764, find the exact values of the six trigonometric functions o...
 6.2.51: In 4764, find the exact values of the six trigonometric functions o...
 6.2.52: In 4764, find the exact values of the six trigonometric functions o...
 6.2.53: In 4764, find the exact values of the six trigonometric functions o...
 6.2.54: In 4764, find the exact values of the six trigonometric functions o...
 6.2.55: In 4764, find the exact values of the six trigonometric functions o...
 6.2.56: In 4764, find the exact values of the six trigonometric functions o...
 6.2.57: In 4764, find the exact values of the six trigonometric functions o...
 6.2.58: In 4764, find the exact values of the six trigonometric functions o...
 6.2.59: In 4764, find the exact values of the six trigonometric functions o...
 6.2.60: In 4764, find the exact values of the six trigonometric functions o...
 6.2.61: In 4764, find the exact values of the six trigonometric functions o...
 6.2.62: In 4764, find the exact values of the six trigonometric functions o...
 6.2.63: In 4764, find the exact values of the six trigonometric functions o...
 6.2.64: In 4764, find the exact values of the six trigonometric functions o...
 6.2.65: In 6576, use a calculator to find the approximate value of each exp...
 6.2.66: In 6576, use a calculator to find the approximate value of each exp...
 6.2.67: In 6576, use a calculator to find the approximate value of each exp...
 6.2.68: In 6576, use a calculator to find the approximate value of each exp...
 6.2.69: In 6576, use a calculator to find the approximate value of each exp...
 6.2.70: In 6576, use a calculator to find the approximate value of each exp...
 6.2.71: In 6576, use a calculator to find the approximate value of each exp...
 6.2.72: In 6576, use a calculator to find the approximate value of each exp...
 6.2.73: In 6576, use a calculator to find the approximate value of each exp...
 6.2.74: In 6576, use a calculator to find the approximate value of each exp...
 6.2.75: In 6576, use a calculator to find the approximate value of each exp...
 6.2.76: In 6576, use a calculator to find the approximate value of each exp...
 6.2.77: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.78: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.79: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.80: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.81: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.82: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.83: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.84: In 7784, a point on the terminal side of an angle u in standard pos...
 6.2.85: Find the exact value of: sin 45 + sin 135 + sin 225 + sin 315 86.
 6.2.86: Find the exact value of: tan 60 + tan 150 8
 6.2.87: Find the exact value of: sin 40 + sin 130 + sin 220 + sin 310 88.
 6.2.88: Find the exact value of: tan 40 + tan 140 8
 6.2.89: If f1u2 = sin u = 0.1, find f1u + p2.
 6.2.90: If f1u2 = cos u = 0.3, find f1u + p2.
 6.2.91: If f1u2 = tan u = 3, find f1u + p2.
 6.2.92: If f1u2 = cot u = 2, find f1u + p2.
 6.2.93: If sin u = 1 5 , find csc u.
 6.2.94: If cos u = 2 3 , find sec u.
 6.2.95: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.96: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.97: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.98: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.99: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.100: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.101: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.102: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.103: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.104: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.105: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.106: In 95106, f1u2 = sin u and g1u2 = cos u. Find the exact value of ea...
 6.2.107: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.108: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.109: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.110: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.111: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.112: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.113: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.114: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.115: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.116: In 107116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = x 2 . ...
 6.2.117: Find two negative and three positive angles, expressed in radians, ...
 6.2.118: Find two negative and three positive angles, expressed in radians, ...
 6.2.119: Use a calculator in radian mode to complete the following table. Wh...
 6.2.120: Use a calculator in radian mode to complete the following table. Wh...
 6.2.121: The projectile is fired at an angle of 45 to the horizontal with an...
 6.2.122: The projectile is fired at an angle of 30 to the horizontal with an...
 6.2.123: The projectile is fired at an angle of 25 to the horizontal with an...
 6.2.124: The projectile is fired at an angle of 50 to the horizontal with an...
 6.2.125: See the figure. a If friction is ignored, the time t (in seconds) r...
 6.2.126: In a certain piston engine, the distance x (in centimeters) from th...
 6.2.127: Two oceanfront homes are located 8 miles apart on a straight stretc...
 6.2.128: A designer of decorative art plans to market solid gold spheres enc...
 6.2.129: 384 CHAPTER 6 Trigonometric Functions velocity of y0 feet per secon...
 6.2.130: If u, 0 6 u 6 p, is the angle between the positive xaxis and a non...
 6.2.131: In 131 and 132, use the figure to approximate the value of the six ...
 6.2.132: In 131 and 132, use the figure to approximate the value of the six ...
 6.2.133: Write a brief paragraph that explains how to quickly compute the tr...
 6.2.134: Write a brief paragraph that explains how to quickly compute the tr...
 6.2.135: How would you explain the meaning of the sine function to a fellow ...
Solutions for Chapter 6.2: Trigonometric Functions: Unit Circle Approach
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 6.2: Trigonometric Functions: Unit Circle Approach
Get Full SolutionsChapter 6.2: Trigonometric Functions: Unit Circle Approach includes 135 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Since 135 problems in chapter 6.2: Trigonometric Functions: Unit Circle Approach have been answered, more than 53425 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351.

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

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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].

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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

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 .

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.

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

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

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

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.