 6.177: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.178: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.179: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.180: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.181: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.182: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.183: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.184: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.185: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.186: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.187: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.188: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.189: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.190: Find all solutions in the interval 0 :::; 8 < 360. If rounding is n...
 6.191: Find all solutions for the following equations. Write your answers ...
 6.192: Find all solutions for the following equations. Write your answers ...
 6.193: Find all solutions for the following equations. Write your answers ...
 6.194: Find all solutions for the following equations. Write your answers ...
 6.195: Find all solutions, to the nearest tenth of a degree, in the interv...
 6.196: Find all solutions, to the nearest tenth of a degree, in the interv...
 6.197: Use your graphing calculator to find all radian solutions in the in...
 6.198: Use your graphing calculator to find all radian solutions in the in...
 6.199: Use your graphing calculator to find all radian solutions in the in...
 6.200: Use your graphing calculator to find all radian solutions in the in...
 6.201: Ferris Wheel In Example 6 of Section 4.5, we found the equation tha...
 6.202: Eliminate the parameter t from each of the following and then sketc...
 6.203: Eliminate the parameter t from each of the following and then sketc...
 6.204: Eliminate the parameter t from each of the following and then sketc...
 6.205: Eliminate the parameter t from each of the following and then sketc...
 6.206: Ferris Wheel A Ferris wheel has a diameter of 180 feet and sits 8 f...
 6.207: If d is the distance that the circle has rolled, then what is the l...
 6.208: Use the lengths a, b, r, and d to find the coordinates of point P. ...
 6.209: Now use right triangle trigonometry to find a and b in terms of rand t
 6.210: Using your answers to Questions 1 through 3, find equations for x a...
 6.211: Suppose that r = 1. Complete the table by finding x and y for each ...
 6.212: Use your graphing calculator to graph the cycloid forO ::s t::s 671...
 6.213: Research the cycloid. What property of the cycloid is Melville refe...
Solutions for Chapter 6: Equations
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter 6: Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 37 problems in chapter 6: Equations have been answered, more than 31979 students have viewed full stepbystep solutions from this chapter. Chapter 6: Equations includes 37 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: . Trigonometry was written by and is associated to the ISBN: 9780495108351.

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

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

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

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).