 147.1: sin x 0.8 if 0 x 360 2.
 147.2: tan x sin x if 0 x 360 3
 147.3: 2 cos x 3 0 if 0 x 360 4.
 147.4: 0.5 cos x 1.4 if 720 x 720 5
 147.5: sin 2x sin x if 0 x 360 6.
 147.6: sin 2x 3 sin x 0 if 360 x 360 L
 147.7: sin = 1 + cos
 147.8: 2 cos2 + 2 = 5 cos
 147.9: 2 sin2  3 sin  2 = 0
 147.10: 2 cos2 + 3 sin  3 = 0
 147.11: PHYSICS According to Snells law, the angle at which light enters wa...
 147.12: 2 cos  1 = 0; 0 < 360
 147.13: 2 sin =  3 ; 180 < < 360
 147.14: 4 sin2 = 1; 180 < < 360 1
 147.15: 4 cos2 = 3; 0 < 360
 147.16: cos 2 + 3 cos  1 = 0
 147.17: 2 sin2  cos  1 = 0
 147.18: cos2  _5 2 cos  _3 2 = 0 1
 147.19: cos = 3 cos  2
 147.20: sin = cos
 147.21: tan = sin
 147.22: sin2  2 sin  3 = 0 2
 147.23: 4 sin2  4 sin + 1 = 0
 147.24: sin2 + cos 2  cos = 0
 147.25: 2 sin2  3 sin  2 = 0
 147.26: sin2 = cos2  1
 147.27: 2 cos2 + cos = 0
 147.28: If h = 3 and P = 2, write the equation for the wave and draw its gr...
 147.29: How many times over the first 10 seconds does the graph predict the...
 147.30: 2 cos2 = sin + 1; 0 < 2
 147.31: sin2  1 = cos2 ; 0 <
 147.32: 2 sin2 + sin = 0; < < 2
 147.33: 2 cos2 = cos ; 0 < 2
 147.34: 4 cos2  4 cos + 1 = 0
 147.35: cos 2 = 1  sin
 147.36: (cos )(sin 2) 2 sin + 2 = 0 3
 147.37: 2 sin2 + (2  1) sin = _ 2 2 S
 147.38: tan2  3 tan = 0 39
 147.39: cos2  _7 2 cos  2 = 0
 147.40: sin 2 + _ 3 2 = 3 sin + cos 41
 147.41: 1  sin2  cos = _3 4
 147.42: sin _ 2 + cos = 1 4
 147.43: sin _ 2 + cos _ 2 = 2
 147.44: 2 sin = sin 2
 147.45: tan2 + 3 = (1 + 3 ) tan L
 147.46: The length of the shadow S of the Memorial depends upon the angle o...
 147.47: Find the angle of inclination that will produce a shadow 560 feet l...
 147.48: OPEN ENDED Write an example of a trigonometric equation that has no...
 147.49: REASONING Explain why the equation sec = 0 has no solutions.
 147.50: CHALLENGE Computer games often use transformations to distort image...
 147.51: REASONING Explain why the number of solutions to the equation sin =...
 147.52: Writing in Math Use the information on page 861 to explain how trig...
 147.53: ACT/SAT Which of the following is not a possible solution of 0 = si...
 147.54: REVIEW The graph of the equation y = 2 cos is shown. Which is a sol...
 147.55: sin = _3 5 ; 0 < < 90
 147.56: cos = _1 2 ; 0 < < 90
 147.57: cos = _5 6 ; 0 < < 90
 147.58: sin = _4 5 ; 0 < < 90
 147.59: sin 240
 147.60: cos 315
 147.61: sin 150
 147.62: Solve ABC. Round measures of sides and angles to the nearest tenth.
Solutions for Chapter 147: Solving Trigonometric Equations
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 147: Solving Trigonometric Equations
Get Full SolutionsAlgebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Chapter 147: Solving Trigonometric Equations includes 62 full stepbystep solutions. Since 62 problems in chapter 147: Solving Trigonometric Equations have been answered, more than 53799 students have viewed full stepbystep solutions from this chapter.

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.)

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

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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

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

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

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

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.

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

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

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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