 4.5.4.5.1: The _______ of a sine or cosine curve represents half the distance ...
 4.5.4.5.2: One period of a sine function is called _______ of the sine curve.
 4.5.4.5.3: The period of a sine or cosine function is given by _______ .
 4.5.4.5.4: The period of a sine or cosine function is given by _______ .
 4.5.4.5.5: In Exercises 314, find the period and amplitude.
 4.5.4.5.6: In Exercises 314, find the period and amplitude.
 4.5.4.5.7: In Exercises 314, find the period and amplitude.
 4.5.4.5.8: In Exercises 314, find the period and amplitude.
 4.5.4.5.9: In Exercises 314, find the period and amplitude.
 4.5.4.5.10: In Exercises 314, find the period and amplitude.
 4.5.4.5.11: In Exercises 314, find the period and amplitude.
 4.5.4.5.12: In Exercises 314, find the period and amplitude.
 4.5.4.5.13: In Exercises 314, find the period and amplitude.
 4.5.4.5.14: In Exercises 314, find the period and amplitude.
 4.5.4.5.15: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.16: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.17: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.18: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.19: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.20: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.21: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.22: In Exercises 1522, describe the relationship between the graphs of ...
 4.5.4.5.23: In Exercises 2326, describe the relationship between the graphs of ...
 4.5.4.5.24: In Exercises 2326, describe the relationship between the graphs of ...
 4.5.4.5.25: In Exercises 2326, describe the relationship between the graphs of ...
 4.5.4.5.26: In Exercises 2326, describe the relationship between the graphs of ...
 4.5.4.5.27: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.28: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.29: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.30: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.31: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.32: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.33: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.34: In Exercises 2734, sketch the graphs of f and g in the same coordin...
 4.5.4.5.35: Conjecture In Exercises 3538, use a graphing utility to graph f and...
 4.5.4.5.36: Conjecture In Exercises 3538, use a graphing utility to graph f and...
 4.5.4.5.37: Conjecture In Exercises 3538, use a graphing utility to graph f and...
 4.5.4.5.38: Conjecture In Exercises 3538, use a graphing utility to graph f and...
 4.5.4.5.39: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.40: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.41: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.42: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.43: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.44: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.45: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.46: In Exercises 3946, sketch the graph of the function by hand. Use a ...
 4.5.4.5.47: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.48: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.49: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.50: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.51: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.52: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.53: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.54: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.55: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.56: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.57: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.58: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.59: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.60: In Exercises 4760, use a graphing utility to graph the function. (I...
 4.5.4.5.61: Graphical Reasoning In Exercises 6164, find a and d for the functio...
 4.5.4.5.62: Graphical Reasoning In Exercises 6164, find a and d for the functio...
 4.5.4.5.63: Graphical Reasoning In Exercises 6164, find a and d for the functio...
 4.5.4.5.64: Graphical Reasoning In Exercises 6164, find a and d for the functio...
 4.5.4.5.65: Graphical Reasoning In Exercises 6568, find a, b, and c for the fun...
 4.5.4.5.66: Graphical Reasoning In Exercises 6568, find a, b, and c for the fun...
 4.5.4.5.67: Graphical Reasoning In Exercises 6568, find a, b, and c for the fun...
 4.5.4.5.68: Graphical Reasoning In Exercises 6568, find a, b, and c for the fun...
 4.5.4.5.69: In Exercises 69 and 70, use a graphing utility to graph and for all...
 4.5.4.5.70: In Exercises 69 and 70, use a graphing utility to graph and for all...
 4.5.4.5.71: Health For a person at rest, the velocity (in liters per second) of...
 4.5.4.5.72: Sales A company that produces snowboards, which are seasonal produc...
 4.5.4.5.73: Recreation You are riding a Ferris wheel. Your height (in feet) abo...
 4.5.4.5.74: Health The pressure (in millimeters of mercury) against the walls o...
 4.5.4.5.75: Fuel Consumption The daily consumption (in gallons) of diesel fuel ...
 4.5.4.5.76: Data Analysis The motion of an oscillating weight suspended from a ...
 4.5.4.5.77: Data Analysis The percent (in decimal form) of the moons face that ...
 4.5.4.5.78: Data Analysis The table shows the average daily high temperatures f...
 4.5.4.5.79: True or False? In Exercises 7981, determine whether the statement i...
 4.5.4.5.80: True or False? In Exercises 7981, determine whether the statement i...
 4.5.4.5.81: True or False? In Exercises 7981, determine whether the statement i...
 4.5.4.5.82: Writing Use a graphing utility to graph the function for different ...
 4.5.4.5.83: In Exercises 8386, determine which function is represented by the g...
 4.5.4.5.84: In Exercises 8386, determine which function is represented by the g...
 4.5.4.5.85: In Exercises 8386, determine which function is represented by the g...
 4.5.4.5.86: In Exercises 8386, determine which function is represented by the g...
 4.5.4.5.87: Exploration In Section 4.2, it was shown that is an even function a...
 4.5.4.5.88: Conjecture If is an even function and g is an odd function, use the...
 4.5.4.5.89: xploration Use a graphing utility to explore the ratio which appear...
 4.5.4.5.90: Exploration Use a graphing utility to explore the ratio which appea...
 4.5.4.5.91: Exploration Using calculus, it can be shown that the sine and cosin...
 4.5.4.5.92: Exploration Use the polynomial approximations found in Exercise 91(...
 4.5.4.5.93: In Exercises 93 and 94, plot the points and find the slope of the l...
 4.5.4.5.94: In Exercises 93 and 94, plot the points and find the slope of the l...
 4.5.4.5.95: In Exercises 95 and 96, convert the angle measure from radians to d...
 4.5.4.5.96: In Exercises 95 and 96, convert the angle measure from radians to d...
 4.5.4.5.97: Make a Decision To work an extended application analyzing the norma...
Solutions for Chapter 4.5: Graphs of Sine and Cosine Functions
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 4.5: Graphs of Sine and Cosine Functions
Get Full SolutionsPrecalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. Since 97 problems in chapter 4.5: Graphs of Sine and Cosine Functions have been answered, more than 33339 students have viewed full stepbystep solutions from this chapter. Chapter 4.5: Graphs of Sine and Cosine Functions includes 97 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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

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).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = 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.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

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.