 7.4.1: sin2 u = 1  cos2 u. (p. 390)
 7.4.2: True or False sin1 u2 + cos 1 u2 = cos u  sin u. (p. 394)
 7.4.3: Suppose that f and g are two functions with the same domain. If f1x...
 7.4.4: an2 u  sec2 u = .
 7.4.5: cos1 u2  cos u = .
 7.4.6: True or False sin1 u2 + sin u = 0 for any value of u.
 7.4.7: True or False In establishing an identity, it is often easiest to j...
 7.4.8: True or False tan u # cos u = sin u for any u 12k + 12 p 2
 7.4.9: In 918, simplify each trigonometric expression by following the ind...
 7.4.10: In 918, simplify each trigonometric expression by following the ind...
 7.4.11: In 918, simplify each trigonometric expression by following the ind...
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 7.4.17: In 918, simplify each trigonometric expression by following the ind...
 7.4.18: In 918, simplify each trigonometric expression by following the ind...
 7.4.19: In 1998, establish each identity.
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 7.4.99: In 99102, show that the functions f and g are identically equal.
 7.4.100: In 99102, show that the functions f and g are identically equal.
 7.4.101: In 99102, show that the functions f and g are identically equal.
 7.4.102: In 99102, show that the functions f and g are identically equal.
 7.4.103: Show 216 + 16 tan2 u = 4 sec u if  p 2 6 u 6 p 2
 7.4.104: Show29 sec2 u  9 = 3 tan u if p u 6 3p 2 .
 7.4.105: A searchlight at the grand opening of a new car dealership casts a ...
 7.4.106: Optical methods of measurement often rely on the interference of tw...
 7.4.107: Write a few paragraphs outlining your strategy for establishing ide...
 7.4.108: Write down the three Pythagorean Identities.
 7.4.109: Why do you think it is usually preferable to start with the side co...
 7.4.110: Make up an identity that is not a Fundamental Identity
Solutions for Chapter 7.4: Trigonometric Identities
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 7.4: Trigonometric Identities
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Chapter 7.4: Trigonometric Identities includes 110 full stepbystep solutions. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. Since 110 problems in chapter 7.4: Trigonometric Identities have been answered, more than 56824 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Column space C (A) =
space of all combinations of the columns of A.

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].

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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.

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.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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 •

Outer product uv T
= column times row = rank one matrix.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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).