 Chapter 14.1: The horizontal translation of a trigonometric function is a(n) ____...
 Chapter 14.2: A reference line about which a graph oscillates is a(n) __________.
 Chapter 14.3: The vertical translation of a trigonometric function is called a(n)...
 Chapter 14.4: The __________ formula can be used to find cos 22 _1 2 .
 Chapter 14.5: The __________ can be used to find sin 60 using 30 as a reference
 Chapter 14.6: The __________ can be used to find the sine or cosine of 75 if the ...
 Chapter 14.7: A(n) __________ is an equation that is true for all values for whic...
 Chapter 14.8: The __________ can be used to find the sine or cosine of 65 if the ...
 Chapter 14.9: The absolute value of half the difference between the maximum value...
 Chapter 14.10: Find the amplitude, if it exists, and period of each function. Then...
 Chapter 14.11: Find the amplitude, if it exists, and period of each function. Then...
 Chapter 14.12: Find the amplitude, if it exists, and period of each function. Then...
 Chapter 14.13: Find the amplitude, if it exists, and period of each function. Then...
 Chapter 14.14: Find the amplitude, if it exists, and period of each function. Then...
 Chapter 14.15: Find the amplitude, if it exists, and period of each function. Then...
 Chapter 14.16: The position of a piston can be modeled using the equation y = A si...
 Chapter 14.17: State the vertical shift, amplitude, period, and phase shift of eac...
 Chapter 14.18: State the vertical shift, amplitude, period, and phase shift of eac...
 Chapter 14.19: State the vertical shift, amplitude, period, and phase shift of eac...
 Chapter 14.20: State the vertical shift, amplitude, period, and phase shift of eac...
 Chapter 14.21: The population of a species of bees varies periodically over the co...
 Chapter 14.22: Find the value of each expression
 Chapter 14.23: Find the value of each expression
 Chapter 14.24: Simplify each expression.
 Chapter 14.25: Simplify each expression.
 Chapter 14.26: Simplify each expression.
 Chapter 14.27: Simplify each expression.
 Chapter 14.28: The magnetic force on a particle can be modeled by the equation F =...
 Chapter 14.29: Verify that each of the following is an identity
 Chapter 14.30: Verify that each of the following is an identity
 Chapter 14.31: Verify that each of the following is an identity
 Chapter 14.32: Verify that each of the following is an identity
 Chapter 14.33: The amount of light passing through a polarization filter can be mo...
 Chapter 14.34: Find the exact value of each expression.
 Chapter 14.35: Find the exact value of each expression.
 Chapter 14.36: Find the exact value of each expression.
 Chapter 14.37: Find the exact value of each expression.
 Chapter 14.38: Find the exact value of each expression.
 Chapter 14.39: Find the exact value of each expression.
 Chapter 14.40: Verify that each of the following is an identity.
 Chapter 14.41: Verify that each of the following is an identity.
 Chapter 14.42: Verify that each of the following is an identity.
 Chapter 14.43: Verify that each of the following is an identity.
 Chapter 14.44: Find the exact values of sin 2, cos 2, sin _ 2 , and cos _ 2 for ea...
 Chapter 14.45: Find the exact values of sin 2, cos 2, sin _ 2 , and cos _ 2 for ea...
 Chapter 14.46: Find the exact values of sin 2, cos 2, sin _ 2 , and cos _ 2 for ea...
 Chapter 14.47: Find the exact values of sin 2, cos 2, sin _ 2 , and cos _ 2 for ea...
 Chapter 14.48: Find all solutions of each equation for the interval 0 < 360.
 Chapter 14.49: Find all solutions of each equation for the interval 0 < 360.
 Chapter 14.50: The horizontal and vertical components of an oblique prism can be m...
Solutions for Chapter Chapter 14: Trigonometric Graphs and Identities
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter Chapter 14: Trigonometric Graphs and Identities
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 50 problems in chapter Chapter 14: Trigonometric Graphs and Identities have been answered, more than 47353 students have viewed full stepbystep solutions from this chapter. Chapter Chapter 14: Trigonometric Graphs and Identities includes 50 full stepbystep solutions. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568.

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

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.

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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.

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

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

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

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

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

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·

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.