 14.3.1: Find the value of each expression.
 14.3.2: Find the value of each expression.
 14.3.3: Find the value of each expression.
 14.3.4: Find the value of each expression.
 14.3.5: Simplify each expression.
 14.3.6: Simplify each expression.
 14.3.7: Simplify each expression.
 14.3.8: Simplify each expression.
 14.3.9: When a person moves along a circular path, the body leans away from...
 14.3.10: Find the value of each expression.
 14.3.11: Find the value of each expression.
 14.3.12: Find the value of each expression.
 14.3.13: Find the value of each expression.
 14.3.14: Find the value of each expression.
 14.3.15: Find the value of each expression.
 14.3.16: Find the value of each expression.
 14.3.17: Find the value of each expression.
 14.3.18: Simplify each expression.
 14.3.19: Simplify each expression.
 14.3.20: Simplify each expression.
 14.3.21: Simplify each expression.
 14.3.22: Simplify each expression.
 14.3.23: Simplify each expression.
 14.3.24: Simplify each expression.
 14.3.25: Simplify each expression.
 14.3.26: Simplify each expression.
 14.3.27: When an alternating current of frequency f and a peak current I pas...
 14.3.28: When an alternating current of frequency f and a peak current I pas...
 14.3.29: Find the value of each expression.
 14.3.30: Find the value of each expression.
 14.3.31: Find the value of each expression.
 14.3.32: Find the value of each expression.
 14.3.33: Simplify each expression.
 14.3.34: Simplify each expression.
 14.3.35: Simplify each expression.
 14.3.36: Refer to Exercise 9. If the sine of the angle of inclination of the...
 14.3.37: What is the velocity of the merrygoround? ab
 14.3.38: If the speed of the merrygoround is 3.6 meters per second, what i...
 14.3.39: Solve the formula in terms of E.
 14.3.40: Is the equation in Exercise 39 equivalent to R2 = _I tan cos E ? Ex...
 14.3.41: Describe how you can determine the quadrant in which the terminal s...
 14.3.42: Write two expressions that are equivalent to tan sin .
 14.3.43: If cot (x) = cot (_ 3 ) and 3 < x < 4, find x.
 14.3.44: If tan = _3 4 , find _sin sec
 14.3.45: Use the information on page 837 to explain how trigonometry can be ...
 14.3.46: If sin x = m and 0 < x < 90, then tan x = A _1 m2 . B _1  m2 m . C...
 14.3.47: If sin x = m and 0 < x < 90, then tan x = A _1 m2 . B _1  m2 m . C...
 14.3.48: State the vertical shift, equation of the midline, amplitude, and p...
 14.3.49: State the vertical shift, equation of the midline, amplitude, and p...
 14.3.50: Find the amplitude, if it exists, and period of each function. Then...
 14.3.51: Find the amplitude, if it exists, and period of each function. Then...
 14.3.52: Find the amplitude, if it exists, and period of each function. Then...
 14.3.53: Find the sum of a geometric series for which a1 48, an 3, and r _1 2 .
 14.3.54: Write an equation of a parabola with focus at (11, 1) and directrix...
 14.3.55: Ms. Granger has taught 288 students at this point in her career. If...
 14.3.56: Name the property illustrated by each statement.
 14.3.57: Name the property illustrated by each statement.
 14.3.58: Name the property illustrated by each statement.
 14.3.59: Name the property illustrated by each statement.
Solutions for Chapter 14.3: Trigonometric Identities
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 14.3: Trigonometric Identities
Get Full SolutionsThis textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. Since 59 problems in chapter 14.3: Trigonometric Identities have been answered, more than 46576 students have viewed full stepbystep solutions from this chapter. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. Chapter 14.3: Trigonometric Identities includes 59 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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).

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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.

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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 •

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

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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