 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 12475 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.

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

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

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.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.