 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 103260 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.

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

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).

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

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.

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

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.

Iterative method.
A sequence of steps intended to approach the desired solution.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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.

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

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

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.

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

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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