 4.1.1: The amplitude of the graphs of the sine and cosine functions is , a...
 4.1.2: For the xvalues 0 to p 2 , the graph of the sine function and that...
 4.1.3: The graph of the sine function crosses the xaxis for all numbers o...
 4.1.4: The domain of both the sine and cosine functions (in interval form)...
 4.1.5: The least positive number x for which cos x = 0 is .
 4.1.6: On the interval 3p, 2p4, the function values of the cosine function...
 4.1.7: Match each function with its graph in choices AF y = sin x
 4.1.8: Match each function with its graph in choices AF y = cos x
 4.1.9: Match each function with its graph in choices AF y = sin 2x
 4.1.10: Match each function with its graph in choices AF y = cos 2x
 4.1.11: Match each function with its graph in choices AF y = 2 sin x
 4.1.12: Match each function with its graph in choices AF y = 2 cos x
 4.1.13: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.14: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.15: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.16: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.17: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.18: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.19: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.20: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.21: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.22: Graph each function over the interval 32p, 2p4. Give the amplitude...
 4.1.23: Graph each function over a twoperiod interval. Give the period and...
 4.1.24: Graph each function over a twoperiod interval. Give the period and...
 4.1.25: Graph each function over a twoperiod interval. Give the period and...
 4.1.26: Graph each function over a twoperiod interval. Give the period and...
 4.1.27: Graph each function over a twoperiod interval. Give the period and...
 4.1.28: Graph each function over a twoperiod interval. Give the period and...
 4.1.29: Graph each function over a twoperiod interval. Give the period and...
 4.1.30: Graph each function over a twoperiod interval. Give the period and...
 4.1.31: Graph each function over a twoperiod interval. Give the period and...
 4.1.32: Graph each function over a twoperiod interval. Give the period and...
 4.1.33: Graph each function over a twoperiod interval. Give the period and...
 4.1.34: Graph each function over a twoperiod interval. Give the period and...
 4.1.35: Graph each function over a twoperiod interval. Give the period and...
 4.1.36: Graph each function over a twoperiod interval. Give the period and...
 4.1.37: Graph each function over a twoperiod interval. Give the period and...
 4.1.38: Graph each function over a twoperiod interval. Give the period and...
 4.1.39: Graph each function over a twoperiod interval. Give the period and...
 4.1.40: Graph each function over a twoperiod interval. Give the period and...
 4.1.41: Determine an equation of the form y = a cos bx or y = a sin bx, whe...
 4.1.42: Determine an equation of the form y = a cos bx or y = a sin bx, whe...
 4.1.43: Determine an equation of the form y = a cos bx or y = a sin bx, whe...
 4.1.44: Determine an equation of the form y = a cos bx or y = a sin bx, whe...
 4.1.45: Determine an equation of the form y = a cos bx or y = a sin bx, whe...
 4.1.46: Determine an equation of the form y = a cos bx or y = a sin bx, whe...
 4.1.47: Average Annual Temperature Scientists believe that the average annu...
 4.1.48: Blood Pressure Variation The graph gives the variation in blood pre...
 4.1.49: The chart shows the tides for Kahului Harbor (on the island of Maui...
 4.1.50: The chart shows the tides for Kahului Harbor (on the island of Maui...
 4.1.51: The chart shows the tides for Kahului Harbor (on the island of Maui...
 4.1.52: The chart shows the tides for Kahului Harbor (on the island of Maui...
 4.1.53: The chart shows the tides for Kahului Harbor (on the island of Maui...
 4.1.54: Solve each problem Activity of a Nocturnal Animal Many activities o...
 4.1.55: Atmospheric Carbon Dioxide At Mauna Loa, Hawaii, atmospheric carbon...
 4.1.56: Atmospheric Carbon Dioxide Refer to Exercise 55. The carbon dioxide...
 4.1.57: Average Daily Temperature The temperature in Anchorage, Alaska, can...
 4.1.58: Fluctuation in the Solar Constant The solar constant S is the amoun...
 4.1.59: Pure sounds produce single sine waves on an oscilloscope. Find the ...
 4.1.60: Pure sounds produce single sine waves on an oscilloscope. Find the ...
 4.1.61: Concept Check Compare the graphs of y = sin 2x and y = 2 sin x over...
 4.1.62: Concept Check Compare the graphs of y = cos 3x and y = 3 cos x over...
 4.1.63: For individual or collaborative investigation (Exercises 6366) Conn...
 4.1.64: For individual or collaborative investigation (Exercises 6366) Conn...
 4.1.65: For individual or collaborative investigation (Exercises 6366) Conn...
 4.1.66: For individual or collaborative investigation (Exercises 6366) Conn...
Solutions for Chapter 4.1: Graphs of the Sine and Cosine Functions
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 4.1: Graphs of the Sine and Cosine Functions
Get Full SolutionsChapter 4.1: Graphs of the Sine and Cosine Functions includes 66 full stepbystep solutions. Trigonometry was written by and is associated to the ISBN: 9780134217437. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. Since 66 problems in chapter 4.1: Graphs of the Sine and Cosine Functions have been answered, more than 25878 students have viewed full stepbystep solutions from this chapter.

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).

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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 .

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

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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).

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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

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·

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.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).