 7.3.1: Solve: 3x  5 = x + 1 (pp. A43A44)
 7.3.2: sina p 4 b = ; cosa 8p 3 b = .
 7.3.3: Find the real solutions of 4x2  x  5 = 0. (pp. A46A47)
 7.3.4: Find the real solutions of x2  x  1 = 0. (pp. A49A51)
 7.3.5: Find the real solutions of 12x  122  312x  12  4 = 0. (pp. A51A52)
 7.3.6: Use a graphing utility to solve 5x3  2 = x  x2 . Round answers to...
 7.3.7: Two solutions of the equation sin u = 1 2 are and .
 7.3.8: All the solutions of the equation sin u = 1 2 are .
 7.3.9: True or False Most trigonometric equations have unique solutions.
 7.3.10: True or False Most trigonometric equations have unique solutions.
 7.3.11: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.12: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.13: In 1134, solve each equation on the interval 0 u 6 2p.
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 7.3.17: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.18: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.19: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.20: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.21: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.22: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.23: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.24: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.25: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.26: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.27: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.28: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.29: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.30: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.31: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.32: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.33: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.34: In 1134, solve each equation on the interval 0 u 6 2p.
 7.3.35: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.36: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.37: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.38: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.39: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.40: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.41: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.42: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.43: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.44: In 35 44, solve each equation. Give a general formula for all the s...
 7.3.45: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.46: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.47: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.48: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.49: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.50: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.51: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.52: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.53: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.54: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.55: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.56: In 4556, use a calculator to solve each equation on the interval 0 ...
 7.3.57: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.58: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.59: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.60: In 57 80, solve each equation on the interval 0 u 6 2p.
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 7.3.64: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.65: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.66: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.67: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.68: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.69: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.70: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.71: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.72: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.73: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.74: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.75: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.76: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.77: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.78: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.79: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.80: In 57 80, solve each equation on the interval 0 u 6 2p.
 7.3.81: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.82: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.83: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.84: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.85: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.86: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.87: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.88: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.89: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.90: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.91: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.92: In 8192, use a graphing utility to solve each equation. Express the...
 7.3.93: What are the zeros of f1x2 = 4 sin2 x  3 on the interval 30, 2p4 ?
 7.3.94: What are the zeros of f1x2 = 2 cos 13x2 + 1 on the interval 30, p4 ?
 7.3.95: f1x2 = 3 sin x (a) Find the zeros of f on the interval 3 2p, 4p4. ...
 7.3.96: f1x2 = 2 cos x (a) Find the zeros of f on the interval 3 2p, 4p4. ...
 7.3.97: f1x2 = 4 tan x (a) Solve f1x2 = 4. ` (b) For what values of x is f...
 7.3.98: f1x2 = cot x (a) Solve f1x2 =  23. `
 7.3.99: (a) Graph f1x2 = 3 sin12x2 + 2 and g1x2 = 7 2 on the same Cartesian...
 7.3.100: (a) Graph f1x2 = 2 cos x 2 + 3 and g1x2 = 4 on the same Cartesian p...
 7.3.101: (a) Graph f1x2 = 4 cos x and g1x2 = 2 cos x + 3 on the same Cartes...
 7.3.102: (a) Graph f1x2 = 2 sin x and g1x2 = 2 sin x + 2 on the same Cartes...
 7.3.103: Blood pressure is a way of measuring the amount of force exerted on...
 7.3.104: In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet...
 7.3.105: An airplane is asked to stay within a holding pattern near Chicagos...
 7.3.106: A golfer hits a golf ball with an initial velocity of 100 miles per...
 7.3.107: In the study of heat transfer, the equation x + tan x = 0 occurs. G...
 7.3.108: Two hallways, one of width 3 feet, the other of width 4 feet, meet ...
 7.3.109: The horizontal distance that a projectile will travel in the air (i...
 7.3.110: Refer to 109. (a) If you can throw a baseball with an initial speed...
 7.3.111: The index of refraction of light in passing from a vacuum into wate...
 7.3.112: The index of refraction of light in passing from a vacuum into dens...
 7.3.113: Ptolemy, who lived in the city of Alexandria in Egypt during the se...
 7.3.114: The speed of yellow sodium light (wavelength, 589 nanometers) in a ...
 7.3.115: A beam of light with a wavelength of 589 nanometers traveling in ai...
 7.3.116: A light ray with a wavelength of 589 nanometers (produced by a sodi...
 7.3.117: A light beam passes through a thick slab of material whose index of...
 7.3.118: If the angle of incidence and the angle of refraction are complemen...
 7.3.119: Explain in your own words how you would use your calculator to solv...
 7.3.120: Provide a justification as to why no further points of intersection...
Solutions for Chapter 7.3: Trigonometric Equations
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 7.3: Trigonometric Equations
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Since 120 problems in chapter 7.3: Trigonometric Equations have been answered, more than 56631 students have viewed full stepbystep solutions from this chapter. Chapter 7.3: Trigonometric Equations includes 120 full stepbystep solutions. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351.

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).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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].

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 .

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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.

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

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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.

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

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

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).