 4.6.Problem 1: Graph y 3 2 x sin x for 2x 2. 1
 4.6.a: We can think of the function y 1 sin x as the sum of what two funct...
 4.6.1: To graph the sum of two functions y y1 y2, at each point add the __...
 4.6.Problem 2: Graph y 2 sin
 4.6.b: How do you graph the function y 1 sin x?
 4.6.2: If y2 is positive, then y1 y2 will lie _______ y1 by a distance equ...
 4.6.Problem 3: Graph y sin x sin 2x for 2x 2. 3
 4.6.c: How do you graph the function y 2 sin x cos 2x?
 4.6.3: If y2 is negative, then y1 y2 will lie _______ y1 by a distance equ...
 4.6.Problem 4: Graph y sin x cos x for 0 x 4.
 4.6.d: What is the period of the function y 2 sin x cos 2x?
 4.6.4: A __________ series can be used to represent certain waveforms as a...
 4.6.Problem 5: Graph y cos x 1 3 cos 3x for 2 x 2. 1
 4.6.5: A (1, 1), B (1, 2) 6
 4.6.6: A (0, 1), B (0, 2) 7.
 4.6.7: (, 0.5), B (, 1) 8. A
 4.6.8: A , 2 2 , B , 2 2 Use a
 4.6.9: 1 sin x
 4.6.10: y 1 cos x
 4.6.11: y 2 cos x 1
 4.6.12: y 2 sin x
 4.6.13: y 4 2 sin x
 4.6.14: y 4 2 cos x
 4.6.15: y x sin x 1
 4.6.16: y x cos x
 4.6.17: y x cos x
 4.6.18: y x cos x
 4.6.19: y x sin x 2
 4.6.20: y x cos x
 4.6.21: y 3 sin x cos 2x
 4.6.22: y 3 cos x sin 2x
 4.6.23: y 2 cos x sin 2x 2
 4.6.24: y 2 sin x cos 2x
 4.6.25: y sin x sin
 4.6.26: y cos x cos
 4.6.27: y cos x cos 2x
 4.6.28: y sin x sin 2x
 4.6.29: y sin x cos 2x
 4.6.30: y cos x sin 2x
 4.6.31: y sin x cos x 3
 4.6.32: y cos x sin x
 4.6.33: Make a table using multiples of /2 for x between 0 and 4to help ske...
 4.6.34: Sketch the graph of y x cos x.
 4.6.35: y 2 cos x
 4.6.36: y 2 sin x
 4.6.37: x 36. y 2 sin x
 4.6.38: y x sin x
 4.6.39: y sin x 2 cos x 4
 4.6.40: y cos x 2 sin x
 4.6.41: y sin 2x 2 sin 3x 4
 4.6.42: y cos 2x 2 cos 3x
 4.6.43: In Example 5 we stated that a square wave can be represented by the...
 4.6.44: The waveform shown in Figure 12, called a sawtooth wave, can be rep...
 4.6.45: Linear Velocity A point moving on the circumference of a circle cov...
 4.6.46: Arc Length A point moves at 65 meters per second on the circumferen...
 4.6.47: Arc Length A point is moving with an angular velocity of 3 radians ...
 4.6.48: Angular Velocity Convert 30 revolutions per minute (rpm) to angular...
 4.6.49: Linear Velocity A point is rotating at 5 revolutions per minute on ...
 4.6.50: Arc Length How far does the tip of a 10centimeter minute hand on a...
 4.6.51: If (3, 5) is a point on the graph of a function y1, and (3, 1) is a...
 4.6.52: Given the graphs of y1 and y2 shown in Figure 13, use addition of y...
Solutions for Chapter 4.6: Graphing Combinations of Functions
Full solutions for Trigonometry  7th Edition
ISBN: 9781111826857
Solutions for Chapter 4.6: Graphing Combinations of Functions
Get Full SolutionsTrigonometry was written by and is associated to the ISBN: 9781111826857. Since 61 problems in chapter 4.6: Graphing Combinations of Functions have been answered, more than 24719 students have viewed full stepbystep solutions from this chapter. Chapter 4.6: Graphing Combinations of Functions includes 61 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

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).

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

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.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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.

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

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·