 113.1: In RST, RS 5 18, RT 5 27, and mR 5 50. Find ST to the nearest integer.
 113.2: The measures of two sides of a triangle are 12.0 inches and 15.0 in...
 113.3: In DEF, DE 5 84, EF 5 76, and DF 5 94. Find, to the nearest degree,...
 113.4: The measures of three sides of a triangle are 22, 46, and 58. Find,...
 113.5: Use the Law of Cosines to show that if the measures of the sides of...
 113.6: In ABC, AB 5 24, AC 5 40, and mA 5 30. a. Find the area of ABC. b. ...
 113.7: The lengths of the sides of a triangle are 8, 11, and 15. a. Find t...
 113.8: In ABC, BC 5 30.0, mA 5 70, and mB 5 55. Find, to the nearest tenth...
 113.9: The measures of two angles of a triangle are 100 and 46. The length...
 113.10: In ABC, a 5 14, b 5 16, and mA 5 48. a. How many different triangle...
 113.11: Show that it is not possible to draw PQR with p 5 12, r 5 15, and m...
 113.12: The measure of a side of a rhombus is 28.0 inches and the measure o...
 113.13: Use the Law of Cosines to find two possible lengths for AB of ABC i...
 113.14: Use the Law of Sines to show that there are two possible triangles ...
 113.15: A vertical pole is braced by two wires that extend from different p...
 113.16: Coastguard station A is 12 miles west of coastguard station B along...
 113.17: In the diagram, ABC is a right triangle with the right angle at C, ...
Solutions for Chapter 113: Trigonometric Applications
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 113: Trigonometric Applications
Get Full SolutionsSince 17 problems in chapter 113: Trigonometric Applications have been answered, more than 31150 students have viewed full stepbystep solutions from this chapter. Chapter 113: Trigonometric Applications includes 17 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This expansive textbook survival guide covers the following chapters and their solutions.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det 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].

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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.

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

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.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(DÂ» O.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.