 Chapter 1: Trigonometric Functions
 Chapter 1.1: Angles
 Chapter 1.2: Angle Relationships and Similar Triangles
 Chapter 1.3: Trigonometric Functions
 Chapter 1.4: Using the Definitions of the Trigonometric Functions
 Chapter 2: Acute Angles and Right Triangles
 Chapter 2.1: Trigonometric Functions of Acute Angles
 Chapter 2.2: Trigonometric Functions of NonAcute Angles
 Chapter 2.3: Approximations of Trigonometric Function Values
 Chapter 2.4: Solutions and Applications of Right Triangles
 Chapter 2.5: Further Applications of Right Triangles
 Chapter 3: Radian Measure and the Unit Circle
 Chapter 3.1: Radian Measure
 Chapter 3.2: Applications of Radian Measure
 Chapter 3.3: The Unit Circle and Circular Functions
 Chapter 3.4: Linear and Angular Speed
 Chapter 4: Graphs of the Circular Functions
 Chapter 4.1: Graphs of the Sine and Cosine Functions
 Chapter 4.2: Translations of the Graphs of the Sine and Cosine Functions
 Chapter 4.3: Graphs of the Tangent and Cotangent Functions
 Chapter 4.4: Graphs of the Secant and Cosecant Functions
 Chapter 4.5: Harmonic Motion
 Chapter 5: Trigonometric Identities
 Chapter 5.1: Fundamental Identities
 Chapter 5.2: Verifying Trigonometric Identities
 Chapter 5.3: Sum and Difference Identities for Cosine
 Chapter 5.4: Sum and Difference Identities for Sine and Tangent
 Chapter 5.5: DoubleAngle Identities
 Chapter 5.6: HalfAngle Identities
 Chapter 6: Inverse Circular Functions and Trigonometric Equations
 Chapter 6.1: Inverse Circular Functions
 Chapter 6.2: Trigonometric Equations I
 Chapter 6.3: Trigonometric Equations II
 Chapter 6.4: Equations Involving Inverse Trigonometric Functions
 Chapter 7.1: Oblique Triangles and the Law of Sines
 Chapter 7.2: The Ambiguous Case of the Law of Sines
 Chapter 7.3: The Law of Cosines
 Chapter 7.4: Geometrically Defined Vectors and Applications
 Chapter 7.5: Algebraically Defined Vectors and the Dot Product
 Chapter 8: Complex Numbers, Polar Equations, and Parametric Equations
 Chapter 8.1: Complex Numbers
 Chapter 8.2: Trigonometric (Polar) Form of Complex Numbers
 Chapter 8.3: The Product and Quotient Theorems
 Chapter 8.4: De Moivres Theorem; Powers and Roots of Complex Numbers
 Chapter 8.5: Polar Equations and Graphs
 Chapter 8.6: Parametric Equations, Graphs, and Applications
Trigonometry 11th Edition  Solutions by Chapter
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Trigonometry  11th Edition  Solutions by Chapter
Get Full SolutionsThis expansive textbook survival guide covers the following chapters: 46. Trigonometry was written by and is associated to the ISBN: 9780134217437. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. Since problems from 46 chapters in Trigonometry have been answered, more than 20374 students have viewed full stepbystep answer. The full stepbystep solution to problem in Trigonometry were answered by , our top Math solution expert on 03/19/18, 04:02PM.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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.

Iterative method.
A sequence of steps intended to approach the desired solution.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Outer product uv T
= column times row = rank one matrix.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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

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

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·

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).