 14.5.1: Find the exact value of each expression.
 14.5.2: Find the exact value of each expression.
 14.5.3: Find the exact value of each expression.
 14.5.4: Find the exact value of each expression.
 14.5.5: Find the exact value of each expression.
 14.5.6: Find the exact value of each expression.
 14.5.7: Determine the exact value of tan in the figure
 14.5.8: Verify that each of the following is an identity.
 14.5.9: Verify that each of the following is an identity.
 14.5.10: Verify that each of the following is an identity.
 14.5.11: Find the exact value of each expression.
 14.5.12: Find the exact value of each expression.
 14.5.13: Find the exact value of each expression.
 14.5.14: Find the exact value of each expression.
 14.5.15: Find the exact value of each expression.
 14.5.16: Find the exact value of each expression.
 14.5.17: Find the exact value of each expression.
 14.5.18: Find the exact value of each expression.
 14.5.19: Find the exact value of each expression.
 14.5.20: Find the exact value of each expression.
 14.5.21: Find the exact value of each expression.
 14.5.22: Find the exact value of each expression.
 14.5.23: For Exercises 2326, use the following information. On December 22, ...
 14.5.24: For Exercises 2326, use the following information. On December 22, ...
 14.5.25: For Exercises 2326, use the following information. On December 22, ...
 14.5.26: For Exercises 2326, use the following information. On December 22, ...
 14.5.27: Verify that each of the following is an identity.
 14.5.28: Verify that each of the following is an identity.
 14.5.29: Verify that each of the following is an identity.
 14.5.30: Verify that each of the following is an identity.
 14.5.31: Verify that each of the following is an identity.
 14.5.32: Verify that each of the following is an identity.
 14.5.33: Verify that each of the following is an identity.
 14.5.34: Verify that each of the following is an identity.
 14.5.35: Draw a graph of the waves when they are combined.
 14.5.36: Refer to the application at the beginning of the lesson. What type ...
 14.5.37: Verify that each of the following is an identity
 14.5.38: Verify that each of the following is an identity
 14.5.39: Verify that each of the following is an identity
 14.5.40: Verify that each of the following is an identity
 14.5.41: Give a counterexample to the statement that sin ( + ) = sin + sin i...
 14.5.42: Determine whether cos (  ) < 1 is sometimes, always, or never true...
 14.5.43: Use the sum and difference formulas for sine and cosine to derive f...
 14.5.44: Use the information on page 848 to explain how the sum and differen...
 14.5.45: Find the exact value of sin . A _ 3 2 B _ 2 2 C _1 2 D _ 3 3 46
 14.5.46: Refer to the figure below. Which equation could be used to find mG?...
 14.5.47: Verify that each of the following is an identity
 14.5.48: Verify that each of the following is an identity
 14.5.49: Verify that each of the following is an identity
 14.5.50: Verify that each of the following is an identity
 14.5.51: Simplify each expression.
 14.5.52: Simplify each expression.
 14.5.53: Simplify each expression.
 14.5.54: Simplify each expression.
 14.5.55: A pilot is flying from Chicago to Columbus, a distance of 300 miles...
 14.5.56: Write 6y2 34x2 204 in standard form.
 14.5.57: Solve each equation.
 14.5.58: Solve each equation.
 14.5.59: Solve each equation.
 14.5.60: Solve each equation.
Solutions for Chapter 14.5: Sum and Differences of Angles Formulas
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 14.5: Sum and Differences of Angles Formulas
Get Full SolutionsCalifornia Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. This expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 14.5: Sum and Differences of Angles Formulas have been answered, more than 42733 students have viewed full stepbystep solutions from this chapter. Chapter 14.5: Sum and Differences of Angles Formulas includes 60 full stepbystep solutions. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1.

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

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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.

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).

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)ยท(b  Ax) = o.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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

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

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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