 4.6.4.1.319: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.320: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.321: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.322: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.323: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.324: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.325: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.326: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.327: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.328: Use addition of ycoordinates to sketch the graph of each of the fo...
 4.6.4.1.329: Sketch the graph of each equation from x = 0 to x 8. y = x + sin 1T
 4.6.4.1.330: Sketch the graph of each equation from x = 0 to x 8. y x + cos 1TX
 4.6.4.1.331: Sketch the graph of each equation from x = 0 to x 8. y = 3 sin x + ...
 4.6.4.1.332: Sketch the graph of each equation from x = 0 to x 8. Y = 3 cos x + ...
 4.6.4.1.333: Sketch the graph of each equation from x = 0 to x 8. y 2 sin x  co...
 4.6.4.1.334: Sketch the graph of each equation from x = 0 to x 8. y = 2 cos x si...
 4.6.4.1.335: Sketch the graph of each equation from x = 0 to x 8. y sm x + SIll 2
 4.6.4.1.336: Sketch the graph of each equation from x = 0 to x 8. y = cos x + cos 2
 4.6.4.1.337: Sketch the graph of each equation from x = 0 to x 8. Y sinx + sin 2x
 4.6.4.1.338: Sketch the graph of each equation from x = 0 to x 8. Y = cosx + cos 2x
 4.6.4.1.339: Sketch the graph of each equation from x = 0 to x 8. Y = cosx + sin2x
 4.6.4.1.340: Sketch the graph of each equation from x = 0 to x 8. y = sm x + "2 ...
 4.6.4.1.341: Sketch the graph of each equation from x = 0 to x 8. y = sin x cosx
 4.6.4.1.342: Sketch the graph of each equation from x = 0 to x 8. y cos x sin x
 4.6.4.1.343: Make a table using mUltiples of 1T12 for x between 0 and 41T to hel...
 4.6.4.1.344: Sketch the graph of y = x cos x.
 4.6.4.1.345: Use your graphing calculator to graph each of the following between...
 4.6.4.1.346: Use your graphing calculator to graph each of the following between...
 4.6.4.1.347: Use your graphing calculator to graph each of the following between...
 4.6.4.1.348: Use your graphing calculator to graph each of the following between...
 4.6.4.1.349: Use your graphing calculator to graph each of the following between...
 4.6.4.1.350: Use your graphing calculator to graph each of the following between...
 4.6.4.1.351: Use your graphing calculator to graph each of the following between...
 4.6.4.1.352: Use your graphing calculator to graph each of the following between...
 4.6.4.1.353: In Example 5 we stated that a square wave can be represented by the...
 4.6.4.1.354: The waveform shown in Figure 12, called a sawtooth wave, can be rep...
 4.6.4.1.355: Linear Velocity A point moving on the circumference of a circle cov...
 4.6.4.1.356: Linear Velocity A point is moving on the circumference of a circle....
 4.6.4.1.357: Arc Length A point is moving with a linear velocity of 20 feet per ...
 4.6.4.1.358: Arc Length A point moves at 65 meters per second on the circumferen...
 4.6.4.1.359: Arc Length A point is moving with an angular velocity of 3 radians ...
 4.6.4.1.360: Angular Velocity Convert 30 revolutions per minute (rpm) to angular...
 4.6.4.1.361: Angular Velocity Convert 120 revolutions per minute to angular velo...
 4.6.4.1.362: Linear Velocity A point is rotating at 5 revolutions per minute on ...
 4.6.4.1.363: Arc Length How far does the tip of a 10centimeter minute hand on a...
 4.6.4.1.364: Arc Length How far does the tip of an 8centimeter hour hand on a c...
Solutions for Chapter 4.6: Graphing and Inverse Functions
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter 4.6: Graphing and Inverse Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Trigonometry was written by and is associated to the ISBN: 9780495108351. Since 46 problems in chapter 4.6: Graphing and Inverse Functions have been answered, more than 32216 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: . Chapter 4.6: Graphing and Inverse Functions includes 46 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues 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.

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.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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

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.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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 .

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.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

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

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