 4.6.4.6.1: The graphs of the tangent, cotangent, secant, and cosecant function...
 4.6.4.6.2: To sketch the graph of a secant or cosecant function, first make a ...
 4.6.4.6.3: To sketch the graph of a secant or cosecant function, first make a ...
 4.6.4.6.4: In Exercises 14, use the graph of the function to answer the follow...
 4.6.4.6.5: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.6: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.7: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.8: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.9: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.10: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.11: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.12: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.13: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.14: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.15: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.16: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.17: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.18: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.19: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.20: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.21: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.22: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.23: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.24: In Exercises 524, sketch the graph of the function. (Include two fu...
 4.6.4.6.25: In Exercises 2530, use a graphing utility to graph the function (in...
 4.6.4.6.26: In Exercises 2530, use a graphing utility to graph the function (in...
 4.6.4.6.27: In Exercises 2530, use a graphing utility to graph the function (in...
 4.6.4.6.28: In Exercises 2530, use a graphing utility to graph the function (in...
 4.6.4.6.29: In Exercises 2530, use a graphing utility to graph the function (in...
 4.6.4.6.30: In Exercises 2530, use a graphing utility to graph the function (in...
 4.6.4.6.31: In Exercises 3134, use a graph of the function to approximate the s...
 4.6.4.6.32: In Exercises 3134, use a graph of the function to approximate the s...
 4.6.4.6.33: In Exercises 3134, use a graph of the function to approximate the s...
 4.6.4.6.34: In Exercises 3134, use a graph of the function to approximate the s...
 4.6.4.6.35: In Exercises 3538, use the graph of the function to determine wheth...
 4.6.4.6.36: In Exercises 3538, use the graph of the function to determine wheth...
 4.6.4.6.37: In Exercises 3538, use the graph of the function to determine wheth...
 4.6.4.6.38: In Exercises 3538, use the graph of the function to determine wheth...
 4.6.4.6.39: In Exercises 3942, use a graphing utility to graph the two equation...
 4.6.4.6.40: In Exercises 3942, use a graphing utility to graph the two equation...
 4.6.4.6.41: In Exercises 3942, use a graphing utility to graph the two equation...
 4.6.4.6.42: In Exercises 3942, use a graphing utility to graph the two equation...
 4.6.4.6.43: In Exercises 4346, match the function with its graph. Describe the ...
 4.6.4.6.44: In Exercises 4346, match the function with its graph. Describe the ...
 4.6.4.6.45: In Exercises 4346, match the function with its graph. Describe the ...
 4.6.4.6.46: In Exercises 4346, match the function with its graph. Describe the ...
 4.6.4.6.47: Conjecture In Exercises 4750, use a graphing utility to graph the f...
 4.6.4.6.48: Conjecture In Exercises 4750, use a graphing utility to graph the f...
 4.6.4.6.49: Conjecture In Exercises 4750, use a graphing utility to graph the f...
 4.6.4.6.50: Conjecture In Exercises 4750, use a graphing utility to graph the f...
 4.6.4.6.51: In Exercises 5154, use a graphing utility to graph the function and...
 4.6.4.6.52: In Exercises 5154, use a graphing utility to graph the function and...
 4.6.4.6.53: In Exercises 5154, use a graphing utility to graph the function and...
 4.6.4.6.54: In Exercises 5154, use a graphing utility to graph the function and...
 4.6.4.6.55: Exploration In Exercises 55 and 56, use a graphing utility to graph...
 4.6.4.6.56: Exploration In Exercises 55 and 56, use a graphing utility to graph...
 4.6.4.6.57: Exploration In Exercises 57 and 58, use a graphing utility to graph...
 4.6.4.6.58: Exploration In Exercises 57 and 58, use a graphing utility to graph...
 4.6.4.6.59: PredatorPrey Model The population P of coyotes (a predator) at tim...
 4.6.4.6.60: Meteorology The normal monthly high temperatures (in degrees Fahren...
 4.6.4.6.61: Distance A plane flying at an altitude of 5 miles over level ground...
 4.6.4.6.62: Television Coverage A television camera is on a reviewing platform ...
 4.6.4.6.63: Harmonic Motion An object weighing pounds is suspended from a ceili...
 4.6.4.6.64: Numerical and Graphical Reasoning A crossed belt connects a 10cent...
 4.6.4.6.65: True or False? In Exercises 65 and 66, determine whether the statem...
 4.6.4.6.66: True or False? In Exercises 65 and 66, determine whether the statem...
 4.6.4.6.67: Graphical Reasoning Consider the functions and on the interval (a) ...
 4.6.4.6.68: Pattern Recognition (a) Use a graphing utility to graph each functi...
 4.6.4.6.69: In Exercises 69 and 70, use a graphing utility to explore the ratio...
 4.6.4.6.70: In Exercises 69 and 70, use a graphing utility to explore the ratio...
 4.6.4.6.71: In Exercises 71 and 72, determine which function is represented by ...
 4.6.4.6.72: In Exercises 71 and 72, determine which function is represented by ...
 4.6.4.6.73: Approximation Using calculus, it can be shown that the tangent func...
 4.6.4.6.74: Approximation Using calculus, it can be shown that the secant funct...
 4.6.4.6.75: In Exercises 7578, identify the rule of algebra illustrated by the ...
 4.6.4.6.76: In Exercises 7578, identify the rule of algebra illustrated by the ...
 4.6.4.6.77: In Exercises 7578, identify the rule of algebra illustrated by the ...
 4.6.4.6.78: In Exercises 7578, identify the rule of algebra illustrated by the ...
 4.6.4.6.79: In Exercises 7982, determine whether the function is onetoone. If...
 4.6.4.6.80: In Exercises 7982, determine whether the function is onetoone. If...
 4.6.4.6.81: In Exercises 7982, determine whether the function is onetoone. If...
 4.6.4.6.82: In Exercises 7982, determine whether the function is onetoone. If...
Solutions for Chapter 4.6: Graphs of Other Trigonometric Functions
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 4.6: Graphs of Other Trigonometric Functions
Get Full SolutionsThis 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. Chapter 4.6: Graphs of Other Trigonometric Functions includes 82 full stepbystep solutions. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. Since 82 problems in chapter 4.6: Graphs of Other Trigonometric Functions have been answered, more than 101952 students have viewed full stepbystep solutions from this chapter.

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).

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

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).

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 •

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

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

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

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).

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 II·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.