 94.1: a. What are two possible measures of u if 0 ,u,360 and sin u5cos u?...
 94.2: What is the value of cos u when tan u is undefined? Justify your an...
 94.3: In 311,P is the point at which the terminal side of an angle in sta...
 94.4: In 311,P is the point at which the terminal side of an angle in sta...
 94.5: In 311,P is the point at which the terminal side of an angle in sta...
 94.6: In 311,P is the point at which the terminal side of an angle in sta...
 94.7: In 311,P is the point at which the terminal side of an angle in sta...
 94.8: In 311,P is the point at which the terminal side of an angle in sta...
 94.9: In 311,P is the point at which the terminal side of an angle in sta...
 94.10: In 311,P is the point at which the terminal side of an angle in sta...
 94.11: In 311,P is the point at which the terminal side of an angle in sta...
 94.12: ,second quadrant
 94.13: In 1320,P is a point on the terminal side of an angle in standard p...
 94.14: In 1320,P is a point on the terminal side of an angle in standard p...
 94.15: In 1320,P is a point on the terminal side of an angle in standard p...
 94.16: In 1320,P is a point on the terminal side of an angle in standard p...
 94.17: In 1320,P is a point on the terminal side of an angle in standard p...
 94.18: In 1320,P is a point on the terminal side of an angle in standard p...
 94.19: In 1320,P is a point on the terminal side of an angle in standard p...
 94.20: In 1320,P is a point on the terminal side of an angle in standard p...
 94.21: In 2126, if u is the measure of AOB, an angle in standard position,...
 94.22: In 2126, if u is the measure of AOB, an angle in standard position,...
 94.23: In 2126, if u is the measure of AOB, an angle in standard position,...
 94.24: In 2126, if u is the measure of AOB, an angle in standard position,...
 94.25: In 2126, if u is the measure of AOB, an angle in standard position,...
 94.26: In 2126, if u is the measure of AOB, an angle in standard position,...
 94.27: When sin u521,find a value of: a. cos u b. tan u c. u
 94.28: When tan u50,find a value of: a. sin u b. cos u c. u
 94.29: When tan u is undefined,find a value of: a. sin u b. cos u c. u
 94.30: Angle ROP is an angle in standard position with mROP 5u ,R(1,0) a p...
 94.31: Use the definitions of sin u and cos u based on the unit circle to ...
 94.32: Show that if ROP is an angle in standard position and mROP 5u,then ...
Solutions for Chapter 94: THE TANGENT FUNCTION
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 94: THE TANGENT FUNCTION
Get Full SolutionsSince 32 problems in chapter 94: THE TANGENT FUNCTION have been answered, more than 29301 students have viewed full stepbystep solutions from this chapter. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 94: THE TANGENT FUNCTION includes 32 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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.

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!).

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > 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.

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).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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

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

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