 5.1: In Exercises 1 and 2, find the measure (if possible) of the complem...
 5.2: In Exercises 1 and 2, find the measure (if possible) of the complem...
 5.3: In Exercises 3 and 4, determine the measure of the positive angle w...
 5.4: In Exercises 3 and 4, determine the measure of the positive angle w...
 5.5: Convert 315 to radian measure.
 5.6: Convert 2 radians to degrees. Round to the nearest hundredth of a d...
 5.7: Find the length of an arc on a circle of radius 3 meters that subte...
 5.8: Find the radian measure of the angle subtended by an arc of length ...
 5.9: A wheel is rotating at 4 revolutions per second. Find the angular s...
 5.10: A wheel with a radius of 9 inches is rotating at 8 revolutions per ...
 5.11: A car with 16inchradius wheels is moving with a speed of 50 mph. ...
 5.12: Let be an acute angle of a right triangle as shown below. Find the ...
 5.13: In Exercises 13 and 14, let be an acute angle of a right triangle a...
 5.14: In Exercises 13 and 14, let be an acute angle of a right triangle a...
 5.15: In Exercises 15 to 18, find the exact value of each expression
 5.16: In Exercises 15 to 18, find the exact value of each expression
 5.17: In Exercises 15 to 18, find the exact value of each expression
 5.18: In Exercises 15 to 18, find the exact value of each expression
 5.19: Find the sin for the angle in standard position with point P(1, 3) ...
 5.20: Find the values of the six trigonometric functions of an angle in s...
 5.21: In Exercises 21 to 24, find the measure of the reference angle for ...
 5.22: In Exercises 21 to 24, find the measure of the reference angle for ...
 5.23: In Exercises 21 to 24, find the measure of the reference angle for ...
 5.24: In Exercises 21 to 24, find the measure of the reference angle for ...
 5.25: Find the exact value of
 5.26: Find the value of each of the following to the nearest tenthousandth.
 5.27: Given find the exact value of
 5.28: Given find the exact value of
 5.29: Given find the exact value of
 5.30: Let W be the wrapping function. Evaluate
 5.31: Is the function defined by even, odd, or neither?
 5.32: In Exercises 32 and 33, use the unit circle to show that each equat...
 5.33: In Exercises 32 and 33, use the unit circle to show that each equat...
 5.34: In Exercises 34 to 39, use trigonometric identities to write each e...
 5.35: In Exercises 34 to 39, use trigonometric identities to write each e...
 5.36: In Exercises 34 to 39, use trigonometric identities to write each e...
 5.37: In Exercises 34 to 39, use trigonometric identities to write each e...
 5.38: In Exercises 34 to 39, use trigonometric identities to write each e...
 5.39: In Exercises 34 to 39, use trigonometric identities to write each e...
 5.40: In Exercises 40 to 45, state the amplitude (if it exists), period, ...
 5.41: In Exercises 40 to 45, state the amplitude (if it exists), period, ...
 5.42: In Exercises 40 to 45, state the amplitude (if it exists), period, ...
 5.43: In Exercises 40 to 45, state the amplitude (if it exists), period, ...
 5.44: In Exercises 40 to 45, state the amplitude (if it exists), period, ...
 5.45: In Exercises 40 to 45, state the amplitude (if it exists), period, ...
 5.46: In Exercises 46 to 67, graph each function
 5.47: In Exercises 46 to 67, graph each function
 5.48: In Exercises 46 to 67, graph each function
 5.49: In Exercises 46 to 67, graph each function
 5.50: In Exercises 46 to 67, graph each function
 5.51: In Exercises 46 to 67, graph each function
 5.52: In Exercises 46 to 67, graph each function
 5.53: In Exercises 46 to 67, graph each function
 5.54: In Exercises 46 to 67, graph each function
 5.55: In Exercises 46 to 67, graph each function
 5.56: In Exercises 46 to 67, graph each function
 5.57: In Exercises 46 to 67, graph each function
 5.58: In Exercises 46 to 67, graph each function
 5.59: In Exercises 46 to 67, graph each function
 5.60: In Exercises 46 to 67, graph each function
 5.61: In Exercises 46 to 67, graph each function
 5.62: In Exercises 46 to 67, graph each function
 5.63: In Exercises 46 to 67, graph each function
 5.64: In Exercises 46 to 67, graph each function
 5.65: In Exercises 46 to 67, graph each function
 5.66: In Exercises 46 to 67, graph each function
 5.67: In Exercises 46 to 67, graph each function
 5.68: Altitude Increase A car climbs a hill that has a constant angle of ...
 5.69: Height of a Tree A tree casts a shadow of 8.55 feet when the angle ...
 5.70: Linear Speeds on a Carousel A carousel has two circular rings of ho...
 5.71: Height of a Building Find the height of a building if the angle of ...
 5.72: 2. Simple Harmonic Motion Find the amplitude, period, and frequency...
 5.73: In Exercises 73 and 74, write an equation for the simple harmonic m...
 5.74: In Exercises 73 and 74, write an equation for the simple harmonic m...
 5.75: Simple Harmonic Motion A mass of 5 kilograms is in equilibrium susp...
 5.76: Damped Harmonic Motion A damped harmonic motion a is modeled by whe...
Solutions for Chapter 5: College Algebra and Trigonometry 7th Edition
Full solutions for College Algebra and Trigonometry  7th Edition
ISBN: 9781439048603
Solutions for Chapter 5
Get Full SolutionsSince 76 problems in chapter 5 have been answered, more than 5945 students have viewed full stepbystep solutions from this chapter. College Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048603. Chapter 5 includes 76 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra and Trigonometry, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

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

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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

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

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = 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.

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

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.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

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.

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

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.