 8.6.1: cos12u2 = cos =  1 = 1  2 u 
 8.6.2: sin2 u 2 = 2
 8.6.3: tan . u 2 = 1  cos u
 8.6.4: True or Falsetan12u2 = 2 tan u 1  tan2 u
 8.6.5: True or False sin12u2 as two equivalent forms:2 sin u cos u and sin...
 8.6.6: True or Falsetan12u2 + tan12u2 = tan14u2
 8.6.7: In 718, use the information given about the angle to find the exact...
 8.6.8: In 718, use the information given about the angle to find the exact...
 8.6.9: In 718, use the information given about the angle to find the exact...
 8.6.10: In 718, use the information given about the angle to find the exact...
 8.6.11: In 718, use the information given about the angle to find the exact...
 8.6.12: In 718, use the information given about the angle to find the exact...
 8.6.13: In 718, use the information given about the angle to find the exact...
 8.6.14: In 718, use the information given about the angle to find the exact...
 8.6.15: In 718, use the information given about the angle to find the exact...
 8.6.16: In 718, use the information given about the angle to find the exact...
 8.6.17: In 718, use the information given about the angle to find the exact...
 8.6.18: In 718, use the information given about the angle to find the exact...
 8.6.19: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.20: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.21: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.22: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.23: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.24: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.25: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.26: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.27: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.28: In 1928, use the Halfangle Formulas to find the exact value of eac...
 8.6.29: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.30: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.31: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.32: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.33: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.34: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.35: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.36: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.37: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.38: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.39: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.40: In 2940, use the figures to evaluate each function given that f1x2 ...
 8.6.41: Show that sin4 u = 3 8  1 2 cos12u2 + 1 8 cos14u2
 8.6.42: Show that sin14u2 = 1cos u214 sin u  8 sin3 u2.
 8.6.43: Develop a formula for as a thirddegree polynomial in the variable ...
 8.6.44: Develop a formula for as a fourthdegree polynomial in the variable...
 8.6.45: Find an expression for as a fifthdegree polynomial in the variable...
 8.6.46: Find an expression for as a fifthdegree polynomial in the variable...
 8.6.47: In 4768, establish each identity
 8.6.48: In 4768, establish each identity
 8.6.49: In 4768, establish each identity
 8.6.50: In 4768, establish each identity
 8.6.51: In 4768, establish each identity
 8.6.52: In 4768, establish each identity
 8.6.53: In 4768, establish each identity
 8.6.54: In 4768, establish each identity
 8.6.55: In 4768, establish each identity
 8.6.56: In 4768, establish each identity
 8.6.57: In 4768, establish each identity
 8.6.58: In 4768, establish each identity
 8.6.59: In 4768, establish each identity
 8.6.60: In 4768, establish each identity
 8.6.61: In 4768, establish each identity
 8.6.62: In 4768, establish each identity
 8.6.63: In 4768, establish each identity
 8.6.64: In 4768, establish each identity
 8.6.65: In 4768, establish each identity
 8.6.66: In 4768, establish each identity
 8.6.67: In 4768, establish each identity
 8.6.68: In 4768, establish each identity
 8.6.69: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.70: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.71: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.72: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.73: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.74: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.75: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.76: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.77: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.78: In 6978,solve each equation on the interval 0 u 6 2p
 8.6.79: In 7990, find the exact value of each expression.
 8.6.80: In 7990, find the exact value of each expression.
 8.6.81: In 7990, find the exact value of each expression.
 8.6.82: In 7990, find the exact value of each expression.
 8.6.83: In 7990, find the exact value of each expression.
 8.6.84: In 7990, find the exact value of each expression.
 8.6.85: In 7990, find the exact value of each expression.
 8.6.86: In 7990, find the exact value of each expression.
 8.6.87: In 7990, find the exact value of each expression.
 8.6.88: In 7990, find the exact value of each expression.
 8.6.89: In 7990, find the exact value of each expression.
 8.6.90: In 7990, find the exact value of each expression.
 8.6.91: In 9193, find the real zeros of each trigonometric function on the ...
 8.6.92: In 9193, find the real zeros of each trigonometric function on the ...
 8.6.93: In 9193, find the real zeros of each trigonometric function on the ...
 8.6.94: Constructing a Rain Gutter A rain gutter is to be constructed of al...
 8.6.95: Laser Projection In a laser projection system, the optical or scann...
 8.6.96: Product of Inertia The product of inertia for an area about incline...
 8.6.97: Projectile Motion An object is propelled upward at an angle to the ...
 8.6.98: Sawtooth Curve An oscilloscope often displays a sawtooth curve. Thi...
 8.6.99: Area of an Isosceles Triangle Show that the area A of an isosceles ...
 8.6.100: Geometry A rectangle is inscribed in a semicircle of radius 1. See ...
 8.6.101: If x = 2 tan u express sin12u2 as a function of x.
 8.6.102: If x = 2 tan u, express as a function of cos12u2
 8.6.103: Find the value of the number C:1 2 sin2 x + C =  1 4 cos12x2
 8.6.104: Find the value of the number C: 1 2 cos2 x + C = 1 4 cos12x2
 8.6.105: If z = tan . a2 show thatsin a = 2z 1 + z2 z = tan .
 8.6.106: If z = tan . a2 show thatcos a = 1  z2 1 + z2 z = tan .
 8.6.107: Graph for by using transformations.f1x2 = sin 0 x 2p 2 x = 1  cos1...
 8.6.108: Repeat forg1x2 = cos2 x.
 8.6.109: Use the fact that to find and cos p 24 sin . p 24 cos p 12 = 1 4 A ...
 8.6.110: Show that and use it to find and6 sin . p 16 cos p 8 = 32 + 22 2
 8.6.111: Show thatsin3 u + sin3 1u + 1202 + sin3 1u + 2402 =  3 4 sin13u2
 8.6.112: If tan u = a tanu3 express tan u3 in terms of a.
 8.6.113: Go to the library and research Chebyshv polynomials.Write a report ...
Solutions for Chapter 8.6: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 8.6
Get Full SolutionsChapter 8.6 includes 113 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Since 113 problems in chapter 8.6 have been answered, more than 57976 students have viewed full stepbystep solutions from this chapter. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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

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

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.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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(D» O.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def 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.

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

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

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).