 7.2.1: In Exercises 1 and 2, fill in the blank(s). 1. The standard form of...
 7.2.2: In Exercises 1 and 2, fill in the blank(s). 1. The standard form of...
 7.2.3: In Exercises 36, one of the cases for the known measures of an obli...
 7.2.4: In Exercises 36, one of the cases for the known measures of an obli...
 7.2.5: In Exercises 36, one of the cases for the known measures of an obli...
 7.2.6: In Exercises 36, one of the cases for the known measures of an obli...
 7.2.7: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.8: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.9: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.10: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.11: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.12: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.13: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.14: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.15: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.16: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.17: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.18: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.19: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.20: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.21: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.22: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.23: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.24: In Exercises 724, use the Law of Cosines to solve the triangle. 7. ...
 7.2.25: In Exercises 2530, complete the table by solving the parallelogram ...
 7.2.26: In Exercises 2530, complete the table by solving the parallelogram ...
 7.2.27: In Exercises 2530, complete the table by solving the parallelogram ...
 7.2.28: In Exercises 2530, complete the table by solving the parallelogram ...
 7.2.29: In Exercises 2530, complete the table by solving the parallelogram ...
 7.2.30: In Exercises 2530, complete the table by solving the parallelogram ...
 7.2.31: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.32: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.33: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.34: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.35: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.36: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.37: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.38: In Exercises 3138, determine whether the Law of Sines or the Law of...
 7.2.39: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.40: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.41: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.42: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.43: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.44: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.45: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.46: In Exercises 39 46, use Herons Area Formula to find the area of the...
 7.2.47: To approximate the length of a marsh, a surveyor walks 380 meters f...
 7.2.48: Determine the angle in the design of the streetlight shown in the f...
 7.2.49: On a map, Minneapolis is 165 millimeters due west of Albany, Phoeni...
 7.2.50: Two ships leave a port at 9 a.m. One travels at a bearing of N 53 W...
 7.2.51: A triangular parcel of ground has sides of lengths 725 feet, 650 fe...
 7.2.52: Q is the midpoint of the line segment PR in the truss rafter shown ...
 7.2.53: A 100foot vertical tower is to be erected on the side of a hill th...
 7.2.54: A 100foot vertical tower is to be erected on the side of a hill th...
 7.2.55: The lengths of the sides of a triangular garden at a university are...
 7.2.56: A parking lot has the shape of a parallelogram. The lengths of two ...
 7.2.57: An engine has a seveninch connecting rod fastened to a crank. (See...
 7.2.58: In a process with continuous paper, the paper passes across three r...
 7.2.59: In Exercises 59 and 60, determine whether the statement is true or ...
 7.2.60: In Exercises 59 and 60, determine whether the statement is true or ...
 7.2.61: Use the Law of Cosines to prove each identity. (a) 1 2 bc(1 + cos A...
 7.2.62: To solve the triangle, would you begin by using the Law of Sines or...
 7.2.63: Describe how the Law of Cosines can be used to solve the ambiguous ...
 7.2.64: Use a halfangle formula and the Law of Cosines to show that, for a...
 7.2.65: In Exercises 6568, evaluate the expression without using a calculat...
 7.2.66: In Exercises 6568, evaluate the expression without using a calculat...
 7.2.67: In Exercises 6568, evaluate the expression without using a calculat...
 7.2.68: In Exercises 6568, evaluate the expression without using a calculat...
Solutions for Chapter 7.2: Additional Topics in Trigonometry
Full solutions for Algebra and Trigonometry: Real Mathematics, Real People  7th Edition
ISBN: 9781305071735
Solutions for Chapter 7.2: Additional Topics in Trigonometry
Get Full SolutionsChapter 7.2: Additional Topics in Trigonometry includes 68 full stepbystep solutions. Algebra and Trigonometry: Real Mathematics, Real People was written by and is associated to the ISBN: 9781305071735. This expansive textbook survival guide covers the following chapters and their solutions. Since 68 problems in chapter 7.2: Additional Topics in Trigonometry have been answered, more than 59232 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry: Real Mathematics, Real People, edition: 7.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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.

Iterative method.
A sequence of steps intended to approach the desired solution.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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.

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

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

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

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

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

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.