 141.1: y = _1 2 sin
 141.2: y = 2 sin
 141.3: y = _2 3 cos
 141.4: y = _1 4 tan
 141.5: y = csc 2
 141.6: y = 4 sin 2
 141.7: y = 4 cos _3 4
 141.8: y = _1 2 sec 3
 141.9: y = _3 4 cos _1 2
 141.10: Determine the period of the function. What does this period represent?
 141.11: What is the maximum number of mice, and when does this occur? 4
 141.12: y = 3 sin
 141.13: y = 5 cos
 141.14: y = 2 csc
 141.15: y = 2 tan
 141.16: y = _1 5 sin
 141.17: y = _1 3 sec
 141.18: y = sin 4
 141.19: y = sin 2
 141.20: y = sec 3
 141.21: y = cot 5
 141.22: y = 4 tan _1 3
 141.23: y = 2 cot _1 2
 141.24: If the amplitude of the sine function is 0.25, write the equations ...
 141.25: How do the periods of the tuning forks compare?
 141.26: y = 6 sin _2 3
 141.27: y = 3 cos _1 2
 141.28: y = 3 csc _1 2
 141.29: y = _1 2 cot 2
 141.30: 2y = tan
 141.31: 3 4 y = _2 3 sin _3 5
 141.32: Draw a graph of a sine function with an amplitude _3 5 and a period...
 141.33: Draw a graph of a cosine function with an amplitude of _7 8 and a p...
 141.34: Graph the functions f(x) = sin x and g(x) = cos x, where x is measu...
 141.35: Identify all asymptotes to the graph of g(x) = sec x.
 141.36: Write an equation for the motion of the buoy. Assume that it is at ...
 141.37: Draw a graph showing the height of the buoy as a function of time.
 141.38: What is the height of the buoy after 12 seconds?
 141.39: OPEN ENDED Write a trigonometric function that has an amplitude of ...
 141.40: REASONING Explain what it means to say that the period of a functio...
 141.41: CHALLENGE A function is called even if the graphs of y = f(x) and y...
 141.42: FIND THE ERROR Dante and Jamile graphed y = 3 cos _2 3 . Who is cor...
 141.43: Writing in Math Use the information on page 822 to explain how you ...
 141.44: ACT/SAT Identify the equation of the graphed function. A y = _1 2 s...
 141.45: REVIEW Refer to the figure below. If tan x = _10 24, what are sin x...
 141.46: x = Sin1 1
 141.47: Arcsin (1) = y
 141.48: Arccos _ 2 2 = x
 141.49: sin 390
 141.50: sin (315)
 141.51: cos 405
 141.52: PROBABILITY There are 8 girls and 8 boys on the Faculty Advisory Bo...
 141.53: Find the first five terms of the sequence in which a1 = 3, an + 1 =...
 141.54: y = x2, y = 3x2
 141.55: y = 3x2, y = 3x2  4 5
 141.56: y = 2x2, y = 2(x +1)2
Solutions for Chapter 141: Graphing Trigonometric Functions
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 141: Graphing Trigonometric Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 141: Graphing Trigonometric Functions includes 56 full stepbystep solutions. Since 56 problems in chapter 141: Graphing Trigonometric Functions have been answered, more than 53358 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302.

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

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

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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.

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.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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.

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

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.

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

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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