- 14-1.1: y = _1 2 sin
- 14-1.2: y = 2 sin
- 14-1.3: y = _2 3 cos
- 14-1.4: y = _1 4 tan
- 14-1.5: y = csc 2
- 14-1.6: y = 4 sin 2
- 14-1.7: y = 4 cos _3 4
- 14-1.8: y = _1 2 sec 3
- 14-1.9: y = _3 4 cos _1 2
- 14-1.10: Determine the period of the function. What does this period represent?
- 14-1.11: What is the maximum number of mice, and when does this occur? 4
- 14-1.12: y = 3 sin
- 14-1.13: y = 5 cos
- 14-1.14: y = 2 csc
- 14-1.15: y = 2 tan
- 14-1.16: y = _1 5 sin
- 14-1.17: y = _1 3 sec
- 14-1.18: y = sin 4
- 14-1.19: y = sin 2
- 14-1.20: y = sec 3
- 14-1.21: y = cot 5
- 14-1.22: y = 4 tan _1 3
- 14-1.23: y = 2 cot _1 2
- 14-1.24: If the amplitude of the sine function is 0.25, write the equations ...
- 14-1.25: How do the periods of the tuning forks compare?
- 14-1.26: y = 6 sin _2 3
- 14-1.27: y = 3 cos _1 2
- 14-1.28: y = 3 csc _1 2
- 14-1.29: y = _1 2 cot 2
- 14-1.30: 2y = tan
- 14-1.31: 3 4 y = _2 3 sin _3 5
- 14-1.32: Draw a graph of a sine function with an amplitude _3 5 and a period...
- 14-1.33: Draw a graph of a cosine function with an amplitude of _7 8 and a p...
- 14-1.34: Graph the functions f(x) = sin x and g(x) = cos x, where x is measu...
- 14-1.35: Identify all asymptotes to the graph of g(x) = sec x.
- 14-1.36: Write an equation for the motion of the buoy. Assume that it is at ...
- 14-1.37: Draw a graph showing the height of the buoy as a function of time.
- 14-1.38: What is the height of the buoy after 12 seconds?
- 14-1.39: OPEN ENDED Write a trigonometric function that has an amplitude of ...
- 14-1.40: REASONING Explain what it means to say that the period of a functio...
- 14-1.41: CHALLENGE A function is called even if the graphs of y = f(x) and y...
- 14-1.42: FIND THE ERROR Dante and Jamile graphed y = 3 cos _2 3 . Who is cor...
- 14-1.43: Writing in Math Use the information on page 822 to explain how you ...
- 14-1.44: ACT/SAT Identify the equation of the graphed function. A y = _1 2 s...
- 14-1.45: REVIEW Refer to the figure below. If tan x = _10 24, what are sin x...
- 14-1.46: x = Sin-1 1
- 14-1.47: Arcsin (-1) = y
- 14-1.48: Arccos _ 2 2 = x
- 14-1.49: sin 390
- 14-1.50: sin (-315)
- 14-1.51: cos 405
- 14-1.52: PROBABILITY There are 8 girls and 8 boys on the Faculty Advisory Bo...
- 14-1.53: Find the first five terms of the sequence in which a1 = 3, an + 1 =...
- 14-1.54: y = x2, y = 3x2
- 14-1.55: y = 3x2, y = 3x2 - 4 5
- 14-1.56: y = 2x2, y = 2(x +1)2
Solutions for Chapter 14-1: Graphing Trigonometric Functions
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2) | 1st Edition
Column space C (A) =
space of all combinations of the columns of A.
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].
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.
Invert A by row operations on [A I] to reach [I A-I].
Gram-Schmidt 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.
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.
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).
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.
Stretch and shift the time axis to create Wjk(t) = woo(2j t - k).