 7.1.1: What is the domain and the range of y = sin x ? (p. 399)
 7.1.2: A suitable restriction on the domain of the function f1x2 = 1x  12...
 7.1.3: If the domain of a onetoone function is 33, 2, the range of its i...
 7.1.4: True or False The graph of y = cos x is decreasing on the interval ...
 7.1.5: tan p 4 = ; sin p 3 = (pp. 373375)
 7.1.6: sina  p 6 b = ; cos p = . (pp. 377378)
 7.1.7: y = sin1 x means , where 1 x 1 and  p 2 y p 2
 7.1.8: cos1 1cos x2 = x where .
 7.1.9: tan1tan1 x2 = x where .
 7.1.10: True or False The domain of y = sin1 x is  p 2 x p 2 .
 7.1.11: True or False sin1sin1 02 = 0 and cos1cos1 02 = 0.
 7.1.12: True or False y = tan1 x means x = tan y, where  6 x 6 and  p 2 ...
 7.1.13: In 1324, find the exact value of each expression.
 7.1.14: In 1324, find the exact value of each expression.
 7.1.15: In 1324, find the exact value of each expression.
 7.1.16: In 1324, find the exact value of each expression.
 7.1.17: In 1324, find the exact value of each expression.
 7.1.18: In 1324, find the exact value of each expression.
 7.1.19: In 1324, find the exact value of each expression.
 7.1.20: In 1324, find the exact value of each expression.
 7.1.21: In 1324, find the exact value of each expression.
 7.1.22: In 1324, find the exact value of each expression.
 7.1.23: In 1324, find the exact value of each expression.
 7.1.24: In 1324, find the exact value of each expression.
 7.1.25: In 2536, use a calculator to find the value of each expression roun...
 7.1.26: In 2536, use a calculator to find the value of each expression roun...
 7.1.27: In 2536, use a calculator to find the value of each expression roun...
 7.1.28: In 2536, use a calculator to find the value of each expression roun...
 7.1.29: In 2536, use a calculator to find the value of each expression roun...
 7.1.30: In 2536, use a calculator to find the value of each expression roun...
 7.1.31: In 2536, use a calculator to find the value of each expression roun...
 7.1.32: In 2536, use a calculator to find the value of each expression roun...
 7.1.33: In 2536, use a calculator to find the value of each expression roun...
 7.1.34: In 2536, use a calculator to find the value of each expression roun...
 7.1.35: In 2536, use a calculator to find the value of each expression roun...
 7.1.36: In 2536, use a calculator to find the value of each expression roun...
 7.1.37: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.38: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.39: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.40: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.41: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.42: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.43: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.44: In 37 44, find the exact value of each expression. Do not use a cal...
 7.1.45: In 4552, find the exact value, if any, of each composite function. ...
 7.1.46: In 4552, find the exact value, if any, of each composite function. ...
 7.1.47: In 4552, find the exact value, if any, of each composite function. ...
 7.1.48: In 4552, find the exact value, if any, of each composite function. ...
 7.1.49: In 4552, find the exact value, if any, of each composite function. ...
 7.1.50: In 4552, find the exact value, if any, of each composite function. ...
 7.1.51: In 4552, find the exact value, if any, of each composite function. ...
 7.1.52: In 4552, find the exact value, if any, of each composite function. ...
 7.1.53: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.54: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.55: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.56: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.57: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.58: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.59: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.60: In 53 60, find the inverse function f 1 of each function f. Find t...
 7.1.61: In 61 68, find the exact solution of each equation.
 7.1.62: In 61 68, find the exact solution of each equation.
 7.1.63: In 61 68, find the exact solution of each equation.
 7.1.64: In 61 68, find the exact solution of each equation.
 7.1.65: In 61 68, find the exact solution of each equation.
 7.1.66: In 61 68, find the exact solution of each equation.
 7.1.67: In 61 68, find the exact solution of each equation.
 7.1.68: In 61 68, find the exact solution of each equation.
 7.1.69: Approximate the number of hours of daylight in Houston, Texas (2945...
 7.1.70: Approximate the number of hours of daylight in New York, New York (...
 7.1.71: Approximate the number of hours of daylight in Honolulu, Hawaii (21...
 7.1.72: Approximate the number of hours of daylight in Anchorage, Alaska (6...
 7.1.73: Approximate the number of hours of daylight at the Equator (0 north...
 7.1.74: Approximate the number of hours of daylight for any location that i...
 7.1.75: Cadillac Mountain, elevation 1530 feet, is located in Acadia Nation...
 7.1.76: Suppose that a movie theater has a screen that is 28 feet tall. Whe...
 7.1.77: The area under the graph of y = 1 1 + x2 and above the xaxis betwe...
 7.1.78: The area under the graph of y = 1 21  x2 and above the xaxis betw...
 7.1.79: Find the shortest distance from Chicago, latitude 4150N, longitude ...
 7.1.80: Find the shortest distance from Honolulu to Melbourne, Australia, l...
Solutions for Chapter 7.1: The Inverse Sine, Cosine, and Tangent Functions
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 7.1: The Inverse Sine, Cosine, and Tangent Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.1: The Inverse Sine, Cosine, and Tangent Functions includes 80 full stepbystep solutions. Since 80 problems in chapter 7.1: The Inverse Sine, Cosine, and Tangent Functions have been answered, more than 53596 students have viewed full stepbystep solutions from this chapter.

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

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.

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

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

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