 7.1  7.3.1: Find the indicated part of each triangle ABC. Find A if B = 30.6_, ...
 7.1  7.3.2: Find the indicated part of each triangle ABC. Find a if A = 144_, c...
 7.1  7.3.3: Find the indicated part of each triangle ABC. Find C if a = 28.4 ft...
 7.1  7.3.4: Find the area of the triangle shown here. 9 7 150
 7.1  7.3.5: Find the area of triangle ABC if a = 19.5 km, b = 21.0 km, and c = ...
 7.1  7.3.6: For triangle ABC with c = 345, a = 534, and C = 25.4_, there are tw...
 7.1  7.3.7: Solve triangle ABC if c = 326, A = 111_, and B = 41.0_.
 7.1  7.3.8: Height of a Balloon The angles of elevation of a hot air balloon fr...
 7.1  7.3.9: Volcano Movement To help predict eruptions from the volcano Mauna L...
 7.1  7.3.10: Distance between Two Towns To find the distance between two small t...
Solutions for Chapter 7.1  7.3: Quiz
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 7.1  7.3: Quiz
Get Full SolutionsChapter 7.1  7.3: Quiz includes 10 full stepbystep solutions. Trigonometry was written by and is associated to the ISBN: 9780321671776. Since 10 problems in chapter 7.1  7.3: Quiz have been answered, more than 35604 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: 10. This expansive textbook survival guide covers the following chapters and their solutions.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column space C (A) =
space of all combinations of the columns of A.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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].

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.

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.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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 •

Outer product uv T
= column times row = rank one matrix.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

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

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

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.