 5.1.1: In Exercises 16, fill in the blank. _______ means measurement of tr...
 5.1.2: In Exercises 16, fill in the blank. A(n) _______ is determined by r...
 5.1.3: In Exercises 16, fill in the blank. An angle with its initial side ...
 5.1.4: In Exercises 16, fill in the blank. Two angles that have the same i...
 5.1.5: In Exercises 16, fill in the blank. . One _______ is the measure of...
 5.1.6: In Exercises 16, fill in the blank. The _______ speed of a particle...
 5.1.7: Is onehalf revolution of a circle equal to 90 or 180?
 5.1.8: What is the sum of two complementary angles in degrees? in radians?
 5.1.9: Are the angles 315 and 225 coterminal?
 5.1.10: Is the angle 2 3 acute or obtuse?
 5.1.11: In Exercises 11 and 12, estimate the number of degrees in the angle.
 5.1.12: In Exercises 11 and 12, estimate the number of degrees in the angle.
 5.1.13: In Exercises 1318, determine the quadrant in which each angle lies....
 5.1.14: In Exercises 1318, determine the quadrant in which each angle lies....
 5.1.15: In Exercises 1318, determine the quadrant in which each angle lies....
 5.1.16: In Exercises 1318, determine the quadrant in which each angle lies....
 5.1.17: In Exercises 1318, determine the quadrant in which each angle lies....
 5.1.18: In Exercises 1318, determine the quadrant in which each angle lies....
 5.1.19: In Exercises 1924, sketch each angle in standard position. 19. (a) ...
 5.1.20: In Exercises 1924, sketch each angle in standard position. 19. (a) ...
 5.1.21: In Exercises 1924, sketch each angle in standard position. 19. (a) ...
 5.1.22: In Exercises 1924, sketch each angle in standard position. 19. (a) ...
 5.1.23: In Exercises 1924, sketch each angle in standard position. 19. (a) ...
 5.1.24: In Exercises 1924, sketch each angle in standard position. 19. (a) ...
 5.1.25: In Exercises 2528, determine two coterminal angles in degree measur...
 5.1.26: In Exercises 2528, determine two coterminal angles in degree measur...
 5.1.27: In Exercises 2528, determine two coterminal angles in degree measur...
 5.1.28: In Exercises 2528, determine two coterminal angles in degree measur...
 5.1.29: In Exercises 2934, use the angleconversion capabilities of a graph...
 5.1.30: In Exercises 2934, use the angleconversion capabilities of a graph...
 5.1.31: In Exercises 2934, use the angleconversion capabilities of a graph...
 5.1.32: In Exercises 2934, use the angleconversion capabilities of a graph...
 5.1.33: In Exercises 2934, use the angleconversion capabilities of a graph...
 5.1.34: In Exercises 2934, use the angleconversion capabilities of a graph...
 5.1.35: In Exercises 3538, find the difference of the angles. Write your an...
 5.1.36: In Exercises 3538, find the difference of the angles. Write your an...
 5.1.37: In Exercises 3538, find the difference of the angles. Write your an...
 5.1.38: In Exercises 3538, find the difference of the angles. Write your an...
 5.1.39: In Exercises 3944, use the angleconversion capabilities of a graph...
 5.1.40: In Exercises 3944, use the angleconversion capabilities of a graph...
 5.1.41: In Exercises 3944, use the angleconversion capabilities of a graph...
 5.1.42: In Exercises 3944, use the angleconversion capabilities of a graph...
 5.1.43: In Exercises 3944, use the angleconversion capabilities of a graph...
 5.1.44: In Exercises 3944, use the angleconversion capabilities of a graph...
 5.1.45: In Exercises 4548, find (if possible) the complement and supplement...
 5.1.46: In Exercises 4548, find (if possible) the complement and supplement...
 5.1.47: In Exercises 4548, find (if possible) the complement and supplement...
 5.1.48: In Exercises 4548, find (if possible) the complement and supplement...
 5.1.49: In Exercises 49 and 50, estimate the angle to the nearest onehalf ...
 5.1.50: In Exercises 49 and 50, estimate the angle to the nearest onehalf ...
 5.1.51: In Exercises 5156, determine the quadrant in which each angle lies....
 5.1.52: In Exercises 5156, determine the quadrant in which each angle lies....
 5.1.53: In Exercises 5156, determine the quadrant in which each angle lies....
 5.1.54: In Exercises 5156, determine the quadrant in which each angle lies....
 5.1.55: In Exercises 5156, determine the quadrant in which each angle lies....
 5.1.56: In Exercises 5156, determine the quadrant in which each angle lies....
 5.1.57: In Exercises 5762, sketch each angle in standard position. 57. (a) ...
 5.1.58: In Exercises 5762, sketch each angle in standard position. 57. (a) ...
 5.1.59: In Exercises 5762, sketch each angle in standard position. 57. (a) ...
 5.1.60: In Exercises 5762, sketch each angle in standard position. 57. (a) ...
 5.1.61: In Exercises 5762, sketch each angle in standard position. 57. (a) ...
 5.1.62: In Exercises 5762, sketch each angle in standard position. 57. (a) ...
 5.1.63: In Exercises 63 66, rewrite each angle in radian measure as a multi...
 5.1.64: In Exercises 63 66, rewrite each angle in radian measure as a multi...
 5.1.65: In Exercises 63 66, rewrite each angle in radian measure as a multi...
 5.1.66: In Exercises 63 66, rewrite each angle in radian measure as a multi...
 5.1.67: In Exercises 6770, rewrite each angle in degree measure. (Do not us...
 5.1.68: In Exercises 6770, rewrite each angle in degree measure. (Do not us...
 5.1.69: In Exercises 6770, rewrite each angle in degree measure. (Do not us...
 5.1.70: In Exercises 6770, rewrite each angle in degree measure. (Do not us...
 5.1.71: In Exercises 71 76, convert the angle measure from degrees to radia...
 5.1.72: In Exercises 71 76, convert the angle measure from degrees to radia...
 5.1.73: In Exercises 71 76, convert the angle measure from degrees to radia...
 5.1.74: In Exercises 71 76, convert the angle measure from degrees to radia...
 5.1.75: In Exercises 71 76, convert the angle measure from degrees to radia...
 5.1.76: In Exercises 71 76, convert the angle measure from degrees to radia...
 5.1.77: In Exercises 7782, convert the angle measure from radians to degree...
 5.1.78: In Exercises 7782, convert the angle measure from radians to degree...
 5.1.79: In Exercises 7782, convert the angle measure from radians to degree...
 5.1.80: In Exercises 7782, convert the angle measure from radians to degree...
 5.1.81: In Exercises 7782, convert the angle measure from radians to degree...
 5.1.82: In Exercises 7782, convert the angle measure from radians to degree...
 5.1.83: In Exercises 83 86, determine two coterminal angles in radian measu...
 5.1.84: In Exercises 83 86, determine two coterminal angles in radian measu...
 5.1.85: In Exercises 83 86, determine two coterminal angles in radian measu...
 5.1.86: In Exercises 83 86, determine two coterminal angles in radian measu...
 5.1.87: In Exercises 8792, find (if possible) the complement and supplement...
 5.1.88: In Exercises 8792, find (if possible) the complement and supplement...
 5.1.89: In Exercises 8792, find (if possible) the complement and supplement...
 5.1.90: In Exercises 8792, find (if possible) the complement and supplement...
 5.1.91: In Exercises 8792, find (if possible) the complement and supplement...
 5.1.92: In Exercises 8792, find (if possible) the complement and supplement...
 5.1.93: In Exercises 93 96, find the radian measure of the central angle of...
 5.1.94: In Exercises 93 96, find the radian measure of the central angle of...
 5.1.95: In Exercises 93 96, find the radian measure of the central angle of...
 5.1.96: In Exercises 93 96, find the radian measure of the central angle of...
 5.1.97: In Exercises 97100, find the length of the arc on a circle of radiu...
 5.1.98: In Exercises 97100, find the length of the arc on a circle of radiu...
 5.1.99: In Exercises 97100, find the length of the arc on a circle of radiu...
 5.1.100: In Exercises 97100, find the length of the arc on a circle of radiu...
 5.1.101: In Exercises 101104, find the radius r of a circle with an arc leng...
 5.1.102: In Exercises 101104, find the radius r of a circle with an arc leng...
 5.1.103: In Exercises 101104, find the radius r of a circle with an arc leng...
 5.1.104: In Exercises 101104, find the radius r of a circle with an arc leng...
 5.1.105: In Exercises 105 and 106, find the distance between the cities. Ass...
 5.1.106: In Exercises 105 and 106, find the distance between the cities. Ass...
 5.1.107: Assuming that Earth is a sphere of radius 6378 kilometers, what is ...
 5.1.108: A voltmeters pointer is 6 centimeters in length (see figure). Find ...
 5.1.109: An electric hoist is used to lift a piece of equipment 2 feet. The ...
 5.1.110: The number of revolutions made by a figure skater for each type of ...
 5.1.111: A satellite in a circular orbit 1250 kilometers above Earth makes o...
 5.1.112: The circular blade on a saw has a diameter of 7.25 inches and rotat...
 5.1.113: A motorcycle wheel has a diameter of 19.5 inches (see figure) and r...
 5.1.114: A computerized spin balance machine rotates a 25inch diameter tire...
 5.1.115: A Bluray disc is approximately 12 centimeters in diameter. The dri...
 5.1.116: The radii of the pedal sprocket, the wheel sprocket, and the wheel ...
 5.1.117: In Exercises 117119, determine whether the statement is true or fal...
 5.1.118: In Exercises 117119, determine whether the statement is true or fal...
 5.1.119: In Exercises 117119, determine whether the statement is true or fal...
 5.1.120: Prove that the area of a circular sector of radius r with central a...
 5.1.121: In Exercises 121 and 122, use the result of Exercise 120 to find th...
 5.1.122: In Exercises 121 and 122, use the result of Exercise 120 to find th...
 5.1.123: The formulas for the area of a circular sector and arc length are A...
 5.1.124: Determine which angles in the figure are coterminal angles with ang...
 5.1.125: In your own words, write a definition of 1 radian.
 5.1.126: In your own words, explain the difference between 1 radian and 1 de...
 5.1.127: In Exercises 127132, sketch the graph of f(x) = x3 and the graph of...
 5.1.128: In Exercises 127132, sketch the graph of f(x) = x3 and the graph of...
 5.1.129: In Exercises 127132, sketch the graph of f(x) = x3 and the graph of...
 5.1.130: In Exercises 127132, sketch the graph of f(x) = x3 and the graph of...
 5.1.131: In Exercises 127132, sketch the graph of f(x) = x3 and the graph of...
 5.1.132: In Exercises 127132, sketch the graph of f(x) = x3 and the graph of...
Solutions for Chapter 5.1: Trigonometric Functions
Full solutions for Algebra and Trigonometry: Real Mathematics, Real People  7th Edition
ISBN: 9781305071735
Solutions for Chapter 5.1: Trigonometric Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 132 problems in chapter 5.1: Trigonometric Functions have been answered, more than 59075 students have viewed full stepbystep solutions from this chapter. Chapter 5.1: Trigonometric Functions includes 132 full stepbystep solutions. Algebra and Trigonometry: Real Mathematics, Real People was written by and is associated to the ISBN: 9781305071735. This textbook survival guide was created for the textbook: Algebra and Trigonometry: Real Mathematics, Real People, edition: 7.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Column space C (A) =
space of all combinations of the columns of A.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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].

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

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.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

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).

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

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.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.