 14.2.1: State the amplitude, period, and phase shift for each function. The...
 14.2.2: State the amplitude, period, and phase shift for each function. The...
 14.2.3: State the amplitude, period, and phase shift for each function. The...
 14.2.4: State the amplitude, period, and phase shift for each function. The...
 14.2.5: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.6: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.7: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.8: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.9: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.10: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.11: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.12: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.13: Determine the vertical shift, amplitu de, and period of a function ...
 14.2.14: Write the equation for the height h of the weight above the floor a...
 14.2.15: Draw a graph of the function you wrote in Exercise 14
 14.2.16: State the amplitude, period, and phase shift for each function. The...
 14.2.17: State the amplitude, period, and phase shift for each function. The...
 14.2.18: State the amplitude, period, and phase shift for each function. The...
 14.2.19: State the amplitude, period, and phase shift for each function. The...
 14.2.20: State the amplitude, period, and phase shift for each function. The...
 14.2.21: State the amplitude, period, and phase shift for each function. The...
 14.2.22: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.23: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.24: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.25: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.26: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.27: State the vertical shift, equation of the midline, amplitude, and p...
 14.2.28: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.29: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.30: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.31: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.32: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.33: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.34: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.35: State the vertical shift, amplitude, period, and phase shift for ea...
 14.2.36: For Exercises 3638, use the following information. The population o...
 14.2.37: For Exercises 3638, use the following information. The population o...
 14.2.38: For Exercises 3638, use the following information. The population o...
 14.2.39: Graph y = 3  _1 2 cos and y = 3 + _1 2 cos ( + ). How do the graph...
 14.2.40: Compare the graphs of y = sin [ _1 4(  _ 2 )] and y = cos [ _1 4(...
 14.2.41: Graph y = 5 + tan ( + _ 4 ). Describe the transformation to the par...
 14.2.42: Draw a graph of the function y = _2 3 cos (  50) + 2. How does thi...
 14.2.43: When represented on oscilloscope, the note A above middle C has a p...
 14.2.44: The height of the water in a harbor rose to a maximum height of 15 ...
 14.2.45: Write the equation of a trigonometric function with a phase shift o...
 14.2.46: The graph of y = cot is a transformation of the graph of y = tan . ...
 14.2.47: Use the information on page 829 to explain how translations of trig...
 14.2.48: Which equation is represented by the graph? A y = cot ( + 45) B y =...
 14.2.49: Refer to the figure below. If c = 14, find the value of b. F _ 3 2 ...
 14.2.50: Find the amplitude, if it exists, and period of each function. Then...
 14.2.51: Find the amplitude, if it exists, and period of each function. Then...
 14.2.52: Find the amplitude, if it exists, and period of each function. Then...
 14.2.53: Find each value.
 14.2.54: Find each value.
 14.2.55: Find each value.
 14.2.56: Find each value.
 14.2.57: Find the total number of diagonals that can be drawn in a decagon.
 14.2.58: Solve each equation. Round to the nearest hundredth.
 14.2.59: Solve each equation. Round to the nearest hundredth.
 14.2.60: Solve each equation. Round to the nearest hundredth.
 14.2.61: Simplify each expression.
 14.2.62: Simplify each expression.
 14.2.63: Simplify each expression.
 14.2.64: Find the value of each function.
 14.2.65: Find the value of each function.
 14.2.66: Find the value of each function.
 14.2.67: Find the value of each function.
 14.2.68: Find the value of each function.
 14.2.69: Find the value of each function.
 14.2.70: Find the value of each function.
 14.2.71: Find the value of each function.
Solutions for Chapter 14.2: Translations of Trigonometric Graphs
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 14.2: Translations of Trigonometric Graphs
Get Full SolutionsCalifornia Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. Since 71 problems in chapter 14.2: Translations of Trigonometric Graphs have been answered, more than 44241 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. Chapter 14.2: Translations of Trigonometric Graphs includes 71 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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

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

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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