 4.4.1: Concept Check In Exercises 14, match each function with its graph f...
 4.4.2: Concept Check In Exercises 14, match each function with its graph f...
 4.4.3: Concept Check In Exercises 14, match each function with its graph f...
 4.4.4: Concept Check In Exercises 14, match each function with its graph f...
 4.4.5: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.6: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.7: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.8: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.9: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.10: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.11: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.12: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.13: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.14: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.15: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.16: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.17: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.18: Graph each function over a oneperiod interval. See Examples 1 and ...
 4.4.19: Connecting Graphs with Equations Determine an equation for each gra...
 4.4.20: Connecting Graphs with Equations Determine an equation for each gra...
 4.4.21: Connecting Graphs with Equations Determine an equation for each gra...
 4.4.22: Connecting Graphs with Equations Determine an equation for each gra...
 4.4.23: Connecting Graphs with Equations Determine an equation for each gra...
 4.4.24: Connecting Graphs with Equations Determine an equation for each gra...
 4.4.25: The tangent and secant functions are undefined for the same values.
 4.4.26: The secant and cosecant functions are undefined for the same values.
 4.4.27: The graph of y = sec x in Figure 37 suggests that sec1x2 = sec x f...
 4.4.28: The graph of y = csc x in Figure 40 suggests that csc1x2 = csc x ...
 4.4.29: Concept Check If c is any number such that 1 6 c 6 1, then how man...
 4.4.30: Concept Check Consider the function g1x2 = 2 csc14x + p2. What is ...
 4.4.31: Show that sec1x2 = sec x by writing sec1x2 as 1 cos1x2 and then ...
 4.4.32: Show that csc1x2 = csc x by writing csc1x2 as 1 sin1x2 and then...
 4.4.33: (Modeling) Distance of a Rotating Beacon In the figure for Exercise...
 4.4.34: Between each pair of successive asymptotes, a portion of the graph ...
 4.4.35: Use a graphing calculator to graph Y1, Y2, and Y1 + Y2 on the same ...
 4.4.36: Use a graphing calculator to graph Y1, Y2, and Y1 + Y2 on the same ...
Solutions for Chapter 4.4: Graphs of the Secant and Cosecant Functions
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 4.4: Graphs of the Secant and Cosecant Functions
Get Full SolutionsTrigonometry was written by and is associated to the ISBN: 9780321671776. This expansive textbook survival guide covers the following chapters and their solutions. Since 36 problems in chapter 4.4: Graphs of the Secant and Cosecant Functions have been answered, more than 34275 students have viewed full stepbystep solutions from this chapter. Chapter 4.4: Graphs of the Secant and Cosecant Functions includes 36 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 10.

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

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Solvable system Ax = b.
The right side b is in the column space of A.

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

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