×
×

# Solutions for Chapter 9: Applications of Trigonometric Functions

## Full solutions for Algebra and Trigonometry | 8th Edition

ISBN: 9780132329033

Solutions for Chapter 9: Applications of Trigonometric Functions

Solutions for Chapter 9
4 5 0 383 Reviews
26
2
##### ISBN: 9780132329033

This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780132329033. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Since 328 problems in chapter 9: Applications of Trigonometric Functions have been answered, more than 58511 students have viewed full step-by-step solutions from this chapter. Chapter 9: Applications of Trigonometric Functions includes 328 full step-by-step solutions.

Key Math Terms and definitions covered in this textbook
• Block matrix.

A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

• 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.)

• 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.

• Complex conjugate

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

• Cramer's Rule for Ax = b.

B j has b replacing column j of A; x j = det B j I det A

• 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.

• Hankel matrix H.

Constant along each antidiagonal; hij depends on i + j.

• Hessenberg matrix H.

Triangular matrix with one extra nonzero adjacent diagonal.

• Indefinite matrix.

A symmetric matrix with eigenvalues of both signs (+ and - ).

• 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.

• Minimal polynomial of A.

The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A - AI) if no eigenvalues are repeated; always meA) divides peA).

• Random matrix rand(n) or randn(n).

MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

• Similar matrices A and B.

Every B = M-I AM has the same eigenvalues as A.

• Singular matrix A.

A square matrix that has no inverse: det(A) = o.

• Special solutions to As = O.

One free variable is Si = 1, other free variables = o.

• Sum V + W of subs paces.

Space of all (v in V) + (w in W). Direct sum: V n W = to}.

• Symmetric factorizations A = LDLT and A = QAQT.

Signs in A = signs in D.

• Symmetric matrix A.

The transpose is AT = A, and aU = a ji. A-I is also symmetric.

• Wavelets Wjk(t).

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

×