 95.1: Explain why sec u cannot equal 0.5.
 95.2: When tan u is undefined,cot u is defined to be equal to 0.Use the f...
 95.3: In 310, the terminal side of ROP in standard position intersects th...
 95.4: In 310, the terminal side of ROP in standard position intersects th...
 95.5: In 310, the terminal side of ROP in standard position intersects th...
 95.6: In 310, the terminal side of ROP in standard position intersects th...
 95.7: In 310, the terminal side of ROP in standard position intersects th...
 95.8: In 310, the terminal side of ROP in standard position intersects th...
 95.9: In 310, the terminal side of ROP in standard position intersects th...
 95.10: In 310, the terminal side of ROP in standard position intersects th...
 95.11: In 1118,P is a point on the terminal side of an angle in standard p...
 95.12: In 1118,P is a point on the terminal side of an angle in standard p...
 95.13: In 1118,P is a point on the terminal side of an angle in standard p...
 95.14: In 1118,P is a point on the terminal side of an angle in standard p...
 95.15: In 1118,P is a point on the terminal side of an angle in standard p...
 95.16: In 1118,P is a point on the terminal side of an angle in standard p...
 95.17: In 1118,P is a point on the terminal side of an angle in standard p...
 95.18: In 1118,P is a point on the terminal side of an angle in standard p...
 95.19: If sin u50,find all possible values of: a. cos u b. tan u c. sec u
 95.20: If cos u50,find all possible values of: a. sin u b. cot u c. csc u
 95.21: If tan u is undefined,find all possible values of: a. cos u b. sin ...
 95.22: If sec u is undefined,find all possible values of sin u.
 95.23: What is the smallest positive value of u such that cos u50?
 95.24: Grace walked within range of a cell phone tower.As soon as her cell...
 95.25: A pole perpendicular to the ground is braced by a wire 13 feet long...
 95.26: . An airplane travels at an altitude of 6 miles.At a point on the g...
 95.27: The equation sin2 u1cos2 u51 is true for all u. a. Use the given eq...
 95.28: Show that cot u 5 for all values of u for which sin u 0.
Solutions for Chapter 95: THE RECIPROCAL TRIGONOMETRIC FUNCTIONS
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 95: THE RECIPROCAL TRIGONOMETRIC FUNCTIONS
Get Full SolutionsThis textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 28 problems in chapter 95: THE RECIPROCAL TRIGONOMETRIC FUNCTIONS have been answered, more than 28443 students have viewed full stepbystep solutions from this chapter. Chapter 95: THE RECIPROCAL TRIGONOMETRIC FUNCTIONS includes 28 full stepbystep solutions. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029.

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.

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

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.

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.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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

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!

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

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.