 6.2.a: What is the first step in solving the equation 2 cos x 1 sec x?
 6.2.1: To solve an equation containing secant, cosecant, or cotangent func...
 6.2.Problem 1: Solve 2
 6.2.b: Why do we need zero on one side of a quadratic equation to solve th...
 6.2.2: For equations containing trigonometric functions with different arg...
 6.2.Problem 2:
 6.2.c: How many solutions between 0 and 2does the equation cos x 0 contain?
 6.2.3: When solving a
 6.2.Problem 3:
 6.2.d: How d
 6.2.4:
 6.2.Problem 4:
 6.2.Problem 5:
 6.2.5: 3 sec 2 6.
 6.2.6: 2 csc 2 7.
 6.2.7: 2 csc 5 3 8. 2
 6.2.8: 23 sec 7 3 9.
 6.2.9: 4 sin 2 csc 0 10.
 6.2.10: 4 cos 3 sec 0 11
 6.2.11: sec 2 tan 0 12.
 6.2.12: csc 2 cot 0 1
 6.2.13: sin 2cos 0 14.
 6.2.14: 2 sin sin 20 1
 6.2.15: 2 sin 1 csc 16.
 6.2.16: 2 cos 1 sec S
 6.2.17: cos 2x 3 sin x 2 0 18
 6.2.18: cos 2x cos x 2 0 1
 6.2.19: cos x cos 2x 0 20
 6.2.20: sin x cos 2x
 6.2.21: 2 cos2 x sin x 1 0 22
 6.2.22: 2 sin2 x cos x 1 0 2
 6.2.23: 4 sin2 x 4 cos x 5 0 24
 6.2.24: 4 cos2 x 4 sin x 5 0 2
 6.2.25: 2 sin x cot x csc x 0 2
 6.2.26: 2 cos x tan x sec x
 6.2.27: sin x cos x 2 28
 6.2.28: sin x cos x 2 Sol
 6.2.29: 3sin cos 3 30. si
 6.2.30: sin 3 cos 3 31. 3s
 6.2.31: 3sin cos 1 32. si
 6.2.32: sin 3 cos 1 33. s
 6.2.33: sin cos 0 34
 6.2.34: sin cos 1 3
 6.2.35: cos cos 1 36.
 6.2.36: cos cos 0
 6.2.37: 6 cos 7 tan sec 38
 6.2.38: 13 cot 11 csc 6 sin
 6.2.39: 18 sec2 17 tan sec 12 0 40.
 6.2.40: 23 csc2 22 cot csc 15 0 41.
 6.2.41: 7 sin2 9 cos 20 42
 6.2.42: 16 cos 218 sin2 0 Wr
 6.2.43: 7
 6.2.44: 8
 6.2.45: 27
 6.2.46: 28
 6.2.47: 35
 6.2.48: 36
 6.2.49: Physiology In the human body, the value of that makes the following...
 6.2.50: Physiology Find the value of that makes the expression in zero, if ...
 6.2.51: 2 sin2 2 cos 1 0 52.
 6.2.52: 2 cos2 2 sin 1 0 53
 6.2.53: cos2 sin 0 54
 6.2.54: sin2 cos 5
 6.2.55: 2 sin2 3 4 cos 56.
 6.2.56: 4 sin 3 2 cos2 Us
 6.2.57: cos x 3 sin x 2 0 58
 6.2.58: 2 cos x sin x 1 0
 6.2.59: sin2 x 3 sin x 1 0 60
 6.2.60: cos2 x 3 cos x 1 0
 6.2.61: sec x 2 cot x
 6.2.62: csc x 3 tan x
 6.2.63: sin
 6.2.64: cos
 6.2.65: tan
 6.2.66: cot
 6.2.67: Graph y 4 sin2
 6.2.68: Graph y 6 cos2 . x 2 x 2
 6.2.69: Use a halfangle formula to find sin 22.5.
 6.2.70: Use a halfangle formula to find cos 15.
 6.2.71: Solve 2 cos 24 sin 1 for 0 360. Which of the following statements a...
 6.2.72: In solving csc 2 cot 0, one of the steps involves solving which equ...
 6.2.73: Solve 3 sin x cos x 1 for 0 x 2. Which of the following statements ...
 6.2.74: Use a graphing calculator to approximate all radian solutions of co...
Solutions for Chapter 6.2: More on Trigonometric Equations
Full solutions for Trigonometry  7th Edition
ISBN: 9781111826857
Solutions for Chapter 6.2: More on Trigonometric Equations
Get Full SolutionsChapter 6.2: More on Trigonometric Equations includes 83 full stepbystep solutions. Since 83 problems in chapter 6.2: More on Trigonometric Equations have been answered, more than 27999 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 7. Trigonometry was written by and is associated to the ISBN: 9781111826857.

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.)

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

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

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.

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

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Solvable system Ax = b.
The right side b is in the column space of A.

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.